LMFDB - Embedded newform 558.2.g.a.439.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(211,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.211"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			439.3
Character	$\chi$	$=$	558.439
Dual form			558.2.g.a.211.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.59012 - 0.686665i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.38064 + 2.39134i) q^{5} +(1.38973 - 1.03375i) q^{6} +(-0.281122 - 0.486917i) q^{7} +1.00000 q^{8} +(2.05698 + 2.18376i) q^{9} +(-1.38064 - 2.39134i) q^{10} -3.99186 q^{11} +(0.200393 + 1.72042i) q^{12} +(0.735188 - 1.27338i) q^{13} +0.562243 q^{14} +(3.83744 - 2.85449i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.03355 + 1.79016i) q^{17} +(-2.91969 + 0.689519i) q^{18} +(1.45518 - 2.52045i) q^{19} +2.76129 q^{20} +(0.112669 + 0.967294i) q^{21} +(1.99593 - 3.45705i) q^{22} +(-1.12187 - 1.94313i) q^{23} +(-1.59012 - 0.686665i) q^{24} +(-1.31235 - 2.27306i) q^{25} +(0.735188 + 1.27338i) q^{26} +(-1.77134 - 4.88491i) q^{27} +(-0.281122 + 0.486917i) q^{28} +(2.14333 - 3.71236i) q^{29} +(0.553341 + 4.75057i) q^{30} +(3.62516 - 4.22590i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(6.34754 + 2.74107i) q^{33} +(-1.03355 - 1.79016i) q^{34} +1.55251 q^{35} +(0.862702 - 2.87328i) q^{36} +(1.82864 - 3.16730i) q^{37} +(1.45518 + 2.52045i) q^{38} +(-2.04343 + 1.52001i) q^{39} +(-1.38064 + 2.39134i) q^{40} +(3.11925 - 5.40270i) q^{41} +(-0.894036 - 0.386072i) q^{42} +(-5.87561 - 10.1769i) q^{43} +(1.99593 + 3.45705i) q^{44} +(-8.06209 + 1.90396i) q^{45} +2.24373 q^{46} +(2.96852 - 5.14163i) q^{47} +(1.38973 - 1.03375i) q^{48} +(3.34194 - 5.78841i) q^{49} +2.62470 q^{50} +(2.87272 - 2.13688i) q^{51} -1.47038 q^{52} +(0.731740 + 1.26741i) q^{53} +(5.11613 + 0.908425i) q^{54} +(5.51133 - 9.54590i) q^{55} +(-0.281122 - 0.486917i) q^{56} +(-4.04462 + 3.00860i) q^{57} +(2.14333 + 3.71236i) q^{58} -1.27123 q^{59} +(-4.39078 - 1.89608i) q^{60} +(-6.92283 + 11.9907i) q^{61} +(1.84716 + 5.25243i) q^{62} +(0.485048 - 1.61548i) q^{63} +1.00000 q^{64} +(2.03006 + 3.51617i) q^{65} +(-5.54760 + 4.12660i) q^{66} +(-2.84476 + 4.92726i) q^{67} +2.06710 q^{68} +(0.449627 + 3.86016i) q^{69} +(-0.776257 + 1.34452i) q^{70} +(2.14830 + 3.72096i) q^{71} +(2.05698 + 2.18376i) q^{72} +(-4.67244 - 8.09290i) q^{73} +(1.82864 + 3.16730i) q^{74} +(0.525970 + 4.51558i) q^{75} -2.91037 q^{76} +(1.12220 + 1.94370i) q^{77} +(-0.294652 - 2.52966i) q^{78} +(0.516125 + 0.893955i) q^{79} +(-1.38064 - 2.39134i) q^{80} +(-0.537638 + 8.98393i) q^{81} +(3.11925 + 5.40270i) q^{82} -2.04433 q^{83} +(0.781366 - 0.581221i) q^{84} +(-2.85393 - 4.94316i) q^{85} +11.7512 q^{86} +(-5.95731 + 4.43136i) q^{87} -3.99186 q^{88} -3.63785 q^{89} +(2.38217 - 7.93395i) q^{90} -0.826708 q^{91} +(-1.12187 + 1.94313i) q^{92} +(-8.66623 + 4.23043i) q^{93} +(2.96852 + 5.14163i) q^{94} +(4.01818 + 6.95968i) q^{95} +(0.200393 + 1.72042i) q^{96} +(-7.94907 + 13.7682i) q^{97} +(3.34194 + 5.78841i) q^{98} +(-8.21118 - 8.71727i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} + 4 q^{3} - 16 q^{4} - q^{5} - 2 q^{6} + q^{7} + 32 q^{8} + 12 q^{9} - q^{10} + 4 q^{11} - 2 q^{12} - 10 q^{13} - 2 q^{14} - 13 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} + 4 q^{19} + 2 q^{20}+ \cdots + 19 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 + 4 * q^3 - 16 * q^4 - q^5 - 2 * q^6 + q^7 + 32 * q^8 + 12 * q^9 - q^10 + 4 * q^11 - 2 * q^12 - 10 * q^13 - 2 * q^14 - 13 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 + 4 * q^19 + 2 * q^20 + 10 * q^21 - 2 * q^22 - q^23 + 4 * q^24 - 19 * q^25 - 10 * q^26 + 7 * q^27 + q^28 - 3 * q^29 + 14 * q^30 - q^31 - 16 * q^32 - 7 * q^33 - 4 * q^34 - 6 * q^36 - 19 * q^37 + 4 * q^38 + 19 * q^39 - q^40 + 10 * q^41 - 11 * q^42 - 13 * q^43 - 2 * q^44 + 14 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 - 13 * q^49 + 38 * q^50 + 20 * q^51 + 20 * q^52 - 7 * q^53 - 17 * q^54 - 11 * q^55 + q^56 - 5 * q^57 - 3 * q^58 + 12 * q^59 - q^60 + 7 * q^61 + 11 * q^62 - 42 * q^63 + 32 * q^64 - 8 * q^65 + 5 * q^66 - 8 * q^67 + 8 * q^68 + 43 * q^69 + 7 * q^71 + 12 * q^72 + 7 * q^73 - 19 * q^74 - 41 * q^75 - 8 * q^76 - q^77 - 11 * q^78 - 34 * q^79 - q^80 + 10 * q^82 - 28 * q^83 + q^84 + 13 * q^85 + 26 * q^86 - 54 * q^87 + 4 * q^88 + 2 * q^89 - 19 * q^90 + 24 * q^91 - q^92 - 15 * q^93 - 6 * q^94 + 21 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + 19 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.59012	−	0.686665i	−0.918058	−	0.396446i
$3$	−1.59012	−	0.686665i	−0.918058	−	0.396446i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.38064	+	2.39134i	−0.617442	+	1.06944i	0.372509	+	0.928029i	$0.378498\pi$
$5$	−1.38064	+	2.39134i	−0.617442	+	1.06944i	−0.989951	+	0.141413i	$0.954836\pi$
$6$	1.38973	−	1.03375i	0.567355	−	0.422029i
$7$	−0.281122	−	0.486917i	−0.106254	−	0.184037i	0.807996	−	0.589188i	$-0.200552\pi$
$7$	−0.281122	−	0.486917i	−0.106254	−	0.184037i	−0.914250	+	0.405151i	$0.867219\pi$
$8$	1.00000			0.353553
$9$	2.05698	+	2.18376i	0.685661	+	0.727921i
$10$	−1.38064	−	2.39134i	−0.436598	−	0.756209i
$11$	−3.99186			−1.20359			−0.601795	−	0.798651i	$-0.705548\pi$
$11$	−3.99186			−1.20359			−0.601795	+	0.798651i	$0.705548\pi$
$12$	0.200393	+	1.72042i	0.0578484	+	0.496642i
$13$	0.735188	−	1.27338i	0.203904	−	0.353173i	−0.745879	−	0.666082i	$-0.767970\pi$
$13$	0.735188	−	1.27338i	0.203904	−	0.353173i	0.949783	+	0.312909i	$0.101304\pi$
$14$	0.562243			0.150266
$15$	3.83744	−	2.85449i	0.990824	−	0.737027i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.03355	+	1.79016i	−0.250673	+	0.434179i	−0.963711	−	0.266946i	$-0.913985\pi$
$17$	−1.03355	+	1.79016i	−0.250673	+	0.434179i	0.713038	+	0.701125i	$0.247319\pi$
$18$	−2.91969	+	0.689519i	−0.688176	+	0.162521i
$19$	1.45518	−	2.52045i	0.333842	−	0.578231i	−0.649420	−	0.760430i	$-0.724988\pi$
$19$	1.45518	−	2.52045i	0.333842	−	0.578231i	0.983262	+	0.182199i	$0.0583215\pi$
$20$	2.76129			0.617442
$21$	0.112669	+	0.967294i	0.0245865	+	0.211081i
$22$	1.99593	−	3.45705i	0.425533	−	0.737045i
$23$	−1.12187	−	1.94313i	−0.233925	−	0.405170i	0.725035	−	0.688712i	$-0.241824\pi$
$23$	−1.12187	−	1.94313i	−0.233925	−	0.405170i	−0.958960	+	0.283542i	$0.908490\pi$
$24$	−1.59012	−	0.686665i	−0.324583	−	0.140165i
$25$	−1.31235	−	2.27306i	−0.262470	−	0.454611i
$26$	0.735188	+	1.27338i	0.144182	+	0.249731i
$27$	−1.77134	−	4.88491i	−0.340895	−	0.940101i
$28$	−0.281122	+	0.486917i	−0.0531270	+	0.0920186i
$29$	2.14333	−	3.71236i	0.398007	−	0.689368i	−0.595473	−	0.803375i	$-0.703035\pi$
$29$	2.14333	−	3.71236i	0.398007	−	0.689368i	0.993480	+	0.114007i	$0.0363686\pi$
$30$	0.553341	+	4.75057i	0.101026	+	0.867331i
$31$	3.62516	−	4.22590i	0.651098	−	0.758994i
$31$	3.62516	−	4.22590i	0.651098	−	0.758994i
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	6.34754	+	2.74107i	1.10497	+	0.477158i
$34$	−1.03355	−	1.79016i	−0.177253	−	0.307011i
$35$	1.55251			0.262423
$36$	0.862702	−	2.87328i	0.143784	−	0.478880i
$37$	1.82864	−	3.16730i	0.300627	−	0.520701i	−0.675651	−	0.737221i	$-0.736137\pi$
$37$	1.82864	−	3.16730i	0.300627	−	0.520701i	0.976278	+	0.216520i	$0.0694708\pi$
$38$	1.45518	+	2.52045i	0.236062	+	0.408871i
$39$	−2.04343	+	1.52001i	−0.327210	+	0.243396i
$40$	−1.38064	+	2.39134i	−0.218299	+	0.378105i
$41$	3.11925	−	5.40270i	0.487145	−	0.843759i	−0.512746	−	0.858540i	$-0.671372\pi$
$41$	3.11925	−	5.40270i	0.487145	−	0.843759i	0.999891	+	0.0147809i	$0.00470509\pi$
$42$	−0.894036	−	0.386072i	−0.137953	−	0.0595723i
$43$	−5.87561	−	10.1769i	−0.896023	−	1.55196i	−0.832534	−	0.553974i	$-0.813111\pi$
$43$	−5.87561	−	10.1769i	−0.896023	−	1.55196i	−0.0634887	−	0.997983i	$-0.520223\pi$
$44$	1.99593	+	3.45705i	0.300897	+	0.521170i
$45$	−8.06209	+	1.90396i	−1.20182	+	0.283825i
$46$	2.24373			0.330820
$47$	2.96852	−	5.14163i	0.433003	−	0.749983i	−0.564127	−	0.825688i	$-0.690787\pi$
$47$	2.96852	−	5.14163i	0.433003	−	0.749983i	0.997130	+	0.0757045i	$0.0241206\pi$
$48$	1.38973	−	1.03375i	0.200590	−	0.149210i
$49$	3.34194	−	5.78841i	0.477420	−	0.826916i
$50$	2.62470			0.371188
$51$	2.87272	−	2.13688i	0.402261	−	0.299223i
$52$	−1.47038			−0.203904
$53$	0.731740	+	1.26741i	0.100512	+	0.174092i	0.911896	−	0.410422i	$-0.134619\pi$
$53$	0.731740	+	1.26741i	0.100512	+	0.174092i	−0.811384	+	0.584514i	$0.801285\pi$
$54$	5.11613	+	0.908425i	0.696217	+	0.123621i
$55$	5.51133	−	9.54590i	0.743147	−	1.28717i
$56$	−0.281122	−	0.486917i	−0.0375664	−	0.0650670i
$57$	−4.04462	+	3.00860i	−0.535724	+	0.398499i
$58$	2.14333	+	3.71236i	0.281433	+	0.487457i
$59$	−1.27123			−0.165501			−0.0827503	−	0.996570i	$-0.526370\pi$
$59$	−1.27123			−0.165501			−0.0827503	+	0.996570i	$0.526370\pi$
$60$	−4.39078	−	1.89608i	−0.566848	−	0.244783i
$61$	−6.92283	+	11.9907i	−0.886378	+	1.53525i	−0.0422512	+	0.999107i	$0.513453\pi$
$61$	−6.92283	+	11.9907i	−0.886378	+	1.53525i	−0.844126	+	0.536144i	$0.819880\pi$
$62$	1.84716	+	5.25243i	0.234589	+	0.667059i
$63$	0.485048	−	1.61548i	0.0611103	−	0.203532i
$64$	1.00000			0.125000
$65$	2.03006	+	3.51617i	0.251798	+	0.436127i
$66$	−5.54760	+	4.12660i	−0.682863	+	0.507949i
$67$	−2.84476	+	4.92726i	−0.347542	+	0.601961i	−0.985812	−	0.167852i	$-0.946317\pi$
$67$	−2.84476	+	4.92726i	−0.347542	+	0.601961i	0.638270	+	0.769813i	$0.279650\pi$
$68$	2.06710			0.250673
$69$	0.449627	+	3.86016i	0.0541287	+	0.464708i
$70$	−0.776257	+	1.34452i	−0.0927804	+	0.160700i
$71$	2.14830	+	3.72096i	0.254956	+	0.441596i	0.964884	−	0.262678i	$-0.0846057\pi$
$71$	2.14830	+	3.72096i	0.254956	+	0.441596i	−0.709928	+	0.704275i	$0.751272\pi$
$72$	2.05698	+	2.18376i	0.242418	+	0.257359i
$73$	−4.67244	−	8.09290i	−0.546868	−	0.947202i	−0.998487	−	0.0549916i	$-0.982487\pi$
$73$	−4.67244	−	8.09290i	−0.546868	−	0.947202i	0.451619	−	0.892211i	$-0.350847\pi$
$74$	1.82864	+	3.16730i	0.212575	+	0.368191i
$75$	0.525970	+	4.51558i	0.0607338	+	0.521415i
$76$	−2.91037			−0.333842
$77$	1.12220	+	1.94370i	0.127886	+	0.221505i
$78$	−0.294652	−	2.52966i	−0.0333628	−	0.286428i
$79$	0.516125	+	0.893955i	0.0580686	+	0.100578i	0.893598	−	0.448867i	$-0.148172\pi$
$79$	0.516125	+	0.893955i	0.0580686	+	0.100578i	−0.835530	+	0.549445i	$0.814839\pi$
$80$	−1.38064	−	2.39134i	−0.154361	−	0.267360i
$81$	−0.537638	+	8.98393i	−0.0597376	+	0.998214i
$82$	3.11925	+	5.40270i	0.344463	+	0.596628i
$83$	−2.04433			−0.224394			−0.112197	−	0.993686i	$-0.535789\pi$
$83$	−2.04433			−0.224394			−0.112197	+	0.993686i	$0.535789\pi$
$84$	0.781366	−	0.581221i	0.0852541	−	0.0634165i
$85$	−2.85393	−	4.94316i	−0.309552	−	0.536161i
$86$	11.7512			1.26717
$87$	−5.95731	+	4.43136i	−0.638691	+	0.475092i
$88$	−3.99186			−0.425533
$89$	−3.63785			−0.385611			−0.192805	−	0.981237i	$-0.561759\pi$
$89$	−3.63785			−0.385611			−0.192805	+	0.981237i	$0.561759\pi$
$90$	2.38217	−	7.93395i	0.251102	−	0.836312i
$91$	−0.826708			−0.0866626
$92$	−1.12187	+	1.94313i	−0.116963	+	0.202585i
$93$	−8.66623	+	4.23043i	−0.898646	+	0.438675i
$94$	2.96852	+	5.14163i	0.306179	+	0.530318i
$95$	4.01818	+	6.95968i	0.412256	+	0.714049i
$96$	0.200393	+	1.72042i	0.0204525	+	0.175590i
$97$	−7.94907	+	13.7682i	−0.807106	+	1.39795i	0.107754	+	0.994178i	$0.465634\pi$
$97$	−7.94907	+	13.7682i	−0.807106	+	1.39795i	−0.914860	+	0.403771i	$0.867699\pi$
$98$	3.34194	+	5.78841i	0.337587	+	0.584718i
$99$	−8.21118	−	8.71727i	−0.825255	−	0.876118i
$100$	−1.31235	+	2.27306i	−0.131235	+	0.227306i
$101$	1.05409	−	1.82574i	0.104886	−	0.181668i	−0.808806	−	0.588076i	$-0.799886\pi$
$101$	1.05409	−	1.82574i	0.104886	−	0.181668i	0.913692	+	0.406408i	$0.133219\pi$
$102$	0.414232	+	3.55629i	0.0410151	+	0.352125i
$103$	5.89275	−	10.2065i	0.580630	−	1.00568i	−0.414775	−	0.909924i	$-0.636140\pi$
$103$	5.89275	−	10.2065i	0.580630	−	1.00568i	0.995405	−	0.0957562i	$-0.0305269\pi$
$104$	0.735188	−	1.27338i	0.0720911	−	0.124865i
$105$	−2.46869	−	1.06606i	−0.240919	−	0.104036i
$106$	−1.46348			−0.142146
$107$	−3.06844	+	5.31470i	−0.296638	+	0.513792i	−0.975365	−	0.220599i	$-0.929199\pi$
$107$	−3.06844	+	5.31470i	−0.296638	+	0.513792i	0.678727	+	0.734391i	$0.262532\pi$
$108$	−3.34478	+	3.97648i	−0.321852	+	0.382637i
$109$	12.8643			1.23218			0.616088	−	0.787677i	$-0.288716\pi$
$109$	12.8643			1.23218			0.616088	+	0.787677i	$0.288716\pi$
$110$	5.51133	+	9.54590i	0.525484	+	0.910166i
$111$	−5.08264	+	3.78073i	−0.482423	+	0.358851i
$112$	0.562243			0.0531270
$113$	6.85988	−	11.8817i	0.645323	−	1.11773i	−0.338903	−	0.940821i	$-0.610056\pi$
$113$	6.85988	−	11.8817i	0.645323	−	1.11773i	0.984227	−	0.176912i	$-0.0566107\pi$
$114$	−0.583216	−	5.00705i	−0.0546232	−	0.468953i
$115$	6.19558			0.577741
$116$	−4.28667			−0.398007
$117$	4.29303	−	1.01385i	0.396891	−	0.0937306i
$118$	0.635617	−	1.10092i	0.0585133	−	0.101348i
$119$	1.16222			0.106540
$120$	3.83744	−	2.85449i	0.350309	−	0.260578i
$121$	4.93492			0.448629
$122$	−6.92283	−	11.9907i	−0.626764	−	1.08559i
$123$	−8.66983	+	6.44908i	−0.781732	+	0.581494i
$124$	−5.47232	−	1.02653i	−0.491428	−	0.0921852i
$125$	−6.55889			−0.586645
$126$	1.15652	+	1.22781i	0.103031	+	0.109382i
$127$	−3.57207	+	6.18701i	−0.316970	+	0.549008i	−0.979854	−	0.199714i	$-0.935999\pi$
$127$	−3.57207	+	6.18701i	−0.316970	+	0.549008i	0.662884	+	0.748722i	$0.269332\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	2.35486	+	20.2170i	0.207334	+	1.78001i
$130$	−4.06013			−0.356097
$131$	3.48452			0.304444			0.152222	−	0.988346i	$-0.451357\pi$
$131$	3.48452			0.304444			0.152222	+	0.988346i	$0.451357\pi$
$132$	−0.799938	−	6.86767i	−0.0696257	−	0.597754i
$133$	−1.63633			−0.141888
$134$	−2.84476	−	4.92726i	−0.245749	−	0.425651i
$135$	14.1271	+	2.50842i	1.21587	+	0.215891i
$136$	−1.03355	+	1.79016i	−0.0886264	+	0.153505i
$137$	1.66890			0.142584			0.0712918	−	0.997456i	$-0.477288\pi$
$137$	1.66890			0.142584			0.0712918	+	0.997456i	$0.477288\pi$
$138$	−3.56781	−	1.54069i	−0.303712	−	0.131152i
$139$	−8.28078	−	14.3427i	−0.702366	−	1.21653i	−0.967634	−	0.252359i	$-0.918793\pi$
$139$	−8.28078	−	14.3427i	−0.702366	−	1.21653i	0.265267	−	0.964175i	$-0.414540\pi$
$140$	−0.776257	−	1.34452i	−0.0656057	−	0.113632i
$141$	−8.25089	+	6.13744i	−0.694850	+	0.516866i
$142$	−4.29659			−0.360562
$143$	−2.93476	+	5.08316i	−0.245417	+	0.425075i
$144$	−2.91969	+	0.689519i	−0.243307	+	0.0574599i
$145$	5.91835	+	10.2509i	0.491493	+	0.851290i
$146$	9.34488			0.773387
$147$	−9.28880	+	6.90950i	−0.766127	+	0.569886i
$148$	−3.65728			−0.300627
$149$	−12.7433			−1.04397			−0.521987	−	0.852953i	$-0.674809\pi$
$149$	−12.7433			−1.04397			−0.521987	+	0.852953i	$0.674809\pi$
$150$	−4.17359	−	1.80229i	−0.340773	−	0.147156i
$151$	−2.16532	+	3.75045i	−0.176212	+	0.305207i	−0.940580	−	0.339573i	$-0.889718\pi$
$151$	−2.16532	+	3.75045i	−0.176212	+	0.305207i	0.764368	+	0.644780i	$0.223051\pi$
$152$	1.45518	−	2.52045i	0.118031	−	0.204436i
$153$	−6.03530	+	1.42531i	−0.487925	+	0.115229i
$154$	−2.24439			−0.180858
$155$	5.10052	+	14.5035i	0.409684	+	1.16495i
$156$	2.33808	+	1.00965i	0.187196	+	0.0808371i
$157$	−11.0809	−	19.1927i	−0.884353	−	1.53174i	−0.846454	−	0.532463i	$-0.821267\pi$
$157$	−11.0809	−	19.1927i	−0.884353	−	1.53174i	−0.0378993	−	0.999282i	$-0.512067\pi$
$158$	−1.03225			−0.0821214
$159$	−0.293270	−	2.51780i	−0.0232579	−	0.199674i
$160$	2.76129			0.218299
$161$	−0.630761	+	1.09251i	−0.0497109	+	0.0861019i
$162$	−7.51149	−	4.95757i	−0.590158	−	0.389504i
$163$	1.82322			0.142806			0.0714029	−	0.997448i	$-0.477252\pi$
$163$	1.82322			0.142806			0.0714029	+	0.997448i	$0.477252\pi$
$164$	−6.23850			−0.487145
$165$	−15.3185	+	11.3947i	−1.19255	+	0.887078i
$166$	1.02216	−	1.77044i	0.0793354	−	0.137413i
$167$	−6.41709			−0.496569			−0.248285	−	0.968687i	$-0.579867\pi$
$167$	−6.41709			−0.496569			−0.248285	+	0.968687i	$0.579867\pi$
$168$	0.112669	+	0.967294i	0.00869263	+	0.0746283i
$169$	5.41900	+	9.38598i	0.416846	+	0.721999i
$170$	5.70787			0.437773
$171$	8.49735	−	2.00675i	0.649809	−	0.153460i
$172$	−5.87561	+	10.1769i	−0.448011	+	0.775978i
$173$	−21.0217			−1.59825			−0.799127	−	0.601163i	$-0.794704\pi$
$173$	−21.0217			−1.59825			−0.799127	+	0.601163i	$0.794704\pi$
$174$	−0.859016	−	7.37486i	−0.0651218	−	0.559087i
$175$	−0.737859	+	1.27801i	−0.0557769	+	0.0966084i
$176$	1.99593	−	3.45705i	0.150449	−	0.260585i
$177$	2.02142	+	0.872911i	0.151939	+	0.0656120i
$178$	1.81892	−	3.15047i	0.136334	−	0.236137i
$179$	7.59632	−	13.1572i	0.567775	−	0.983416i	−0.429010	−	0.903300i	$-0.641138\pi$
$179$	7.59632	−	13.1572i	0.567775	−	0.983416i	0.996786	−	0.0801160i	$-0.0255291\pi$
$180$	5.67992	+	6.02999i	0.423356	+	0.449449i
$181$	−1.37767	−	2.38619i	−0.102401	−	0.177364i	0.810272	−	0.586054i	$-0.199319\pi$
$181$	−1.37767	−	2.38619i	−0.102401	−	0.177364i	−0.912674	+	0.408689i	$0.865986\pi$
$182$	0.413354	−	0.715950i	0.0306398	−	0.0530698i
$183$	19.2417	−	14.3130i	1.42239	−	1.05805i
$184$	−1.12187	−	1.94313i	−0.0827050	−	0.143249i
$185$	5.04940	+	8.74582i	0.371239	+	0.643005i
$186$	0.669452	−	9.62039i	0.0490866	−	0.705401i
$187$	4.12579	−	7.14608i	0.301708	−	0.522573i
$188$	−5.93704			−0.433003
$189$	−1.88058	+	2.23575i	−0.136792	+	0.162627i
$190$	−8.03635			−0.583018
$191$	17.6085			1.27411			0.637054	−	0.770819i	$-0.280153\pi$
$191$	17.6085			1.27411			0.637054	+	0.770819i	$0.280153\pi$
$192$	−1.59012	−	0.686665i	−0.114757	−	0.0495557i
$193$	4.22580			0.304180			0.152090	−	0.988367i	$-0.451400\pi$
$193$	4.22580			0.304180			0.152090	+	0.988367i	$0.451400\pi$
$194$	−7.94907	−	13.7682i	−0.570710	−	0.988499i
$195$	−0.813619	−	6.98512i	−0.0582645	−	0.500215i
$196$	−6.68388			−0.477420
$197$	−11.0548	−	19.1475i	−0.787624	−	1.36421i	−0.927419	−	0.374025i	$-0.877978\pi$
$197$	−11.0548	−	19.1475i	−0.787624	−	1.36421i	0.139794	−	0.990181i	$-0.455356\pi$
$198$	11.6550	−	2.75246i	0.828282	−	0.195609i
$199$	−4.22595	−	7.31956i	−0.299570	−	0.518870i	0.676468	−	0.736472i	$-0.263510\pi$
$199$	−4.22595	−	7.31956i	−0.299570	−	0.518870i	−0.976038	+	0.217602i	$0.930176\pi$
$200$	−1.31235	−	2.27306i	−0.0927971	−	0.160729i
$201$	7.90689	−	5.88156i	0.557709	−	0.414853i
$202$	1.05409	+	1.82574i	0.0741655	+	0.128458i
$203$	−2.41015			−0.169159
$204$	−3.28695	−	1.41941i	−0.230133	−	0.0993784i
$205$	8.61313	+	14.9184i	0.601567	+	1.04195i
$206$	5.89275	+	10.2065i	0.410567	+	0.711123i
$207$	1.93567	−	6.44687i	0.134538	−	0.448088i
$208$	0.735188	+	1.27338i	0.0509761	+	0.0882932i
$209$	−5.80888	+	10.0613i	−0.401809	+	0.695953i
$210$	2.15758	−	1.60492i	0.148887	−	0.110750i
$211$	26.7357			1.84056			0.920280	−	0.391261i	$-0.127961\pi$
$211$	26.7357			1.84056			0.920280	+	0.391261i	$0.127961\pi$
$212$	0.731740	−	1.26741i	0.0502561	−	0.0870461i
$213$	−0.861005	−	7.39194i	−0.0589951	−	0.506487i
$214$	−3.06844	−	5.31470i	−0.209755	−	0.363306i
$215$	32.4485			2.21297
$216$	−1.77134	−	4.88491i	−0.120525	−	0.332376i
$217$	−3.07677	−	0.577160i	−0.208865	−	0.0391802i
$218$	−6.43215	+	11.1408i	−0.435640	+	0.754551i
$219$	1.87264	+	16.0771i	0.126542	+	1.08639i
$220$	−11.0227			−0.743147
$221$	1.51971	+	2.63221i	0.102227	+	0.177062i
$222$	−0.732892	−	6.29206i	−0.0491885	−	0.422295i
$223$	−10.6257	−	18.4043i	−0.711551	−	1.23244i	−0.964275	−	0.264904i	$-0.914660\pi$
$223$	−10.6257	−	18.4043i	−0.711551	−	1.23244i	0.252723	−	0.967539i	$-0.418674\pi$
$224$	−0.281122	+	0.486917i	−0.0187832	+	0.0325335i
$225$	2.26433	−	7.54150i	0.150956	−	0.502766i
$226$	6.85988	+	11.8817i	0.456312	+	0.790356i
$227$	−26.5385			−1.76142			−0.880711	−	0.473655i	$-0.842934\pi$
$227$	−26.5385			−1.76142			−0.880711	+	0.473655i	$0.842934\pi$
$228$	4.62784	+	1.99845i	0.306486	+	0.132350i
$229$	−2.02883			−0.134069			−0.0670344	−	0.997751i	$-0.521354\pi$
$229$	−2.02883			−0.134069			−0.0670344	+	0.997751i	$0.521354\pi$
$230$	−3.09779	+	5.36553i	−0.204262	+	0.353793i
$231$	−0.449760	−	3.86130i	−0.0295920	−	0.254055i
$232$	2.14333	−	3.71236i	0.140717	−	0.243728i
$233$	12.9457			0.848098			0.424049	−	0.905639i	$-0.360608\pi$
$233$	12.9457			0.848098			0.424049	+	0.905639i	$0.360608\pi$
$234$	−1.26850	+	4.22480i	−0.0829242	+	0.276184i
$235$	8.19693	+	14.1975i	0.534709	+	0.926143i
$236$	0.635617	+	1.10092i	0.0413751	+	0.0716638i
$237$	−0.206855	−	1.77590i	−0.0134367	−	0.115357i
$238$	−0.581108	+	1.00651i	−0.0376676	+	0.0652422i
$239$	−6.91699	+	11.9806i	−0.447423	+	0.774959i	−0.998217	−	0.0596818i	$-0.980991\pi$
$239$	−6.91699	+	11.9806i	−0.447423	+	0.774959i	0.550795	+	0.834641i	$0.314325\pi$
$240$	0.553341	+	4.75057i	0.0357180	+	0.306648i
$241$	13.9301	+	24.1277i	0.897317	+	1.55420i	0.830910	+	0.556407i	$0.187820\pi$
$241$	13.9301	+	24.1277i	0.897317	+	1.55420i	0.0664072	+	0.997793i	$0.478846\pi$
$242$	−2.46746	+	4.27376i	−0.158614	+	0.274728i
$243$	7.02386	−	13.9164i	0.450581	−	0.892736i
$244$	13.8457			0.886378
$245$	9.22805	+	15.9835i	0.589559	+	1.02115i
$246$	−1.25015	−	10.7328i	−0.0797066	−	0.684300i
$247$	−2.13966	−	3.70601i	−0.136144	−	0.235808i
$248$	3.62516	−	4.22590i	0.230198	−	0.268345i
$249$	3.25074	+	1.40377i	0.206007	+	0.0889602i
$250$	3.27944	−	5.68016i	0.207410	−	0.359245i
$251$	4.36267	−	7.55637i	0.275370	−	0.476954i	−0.694859	−	0.719146i	$-0.744533\pi$
$251$	4.36267	−	7.55637i	0.275370	−	0.476954i	0.970228	+	0.242192i	$0.0778665\pi$
$252$	−1.64157	+	0.387677i	−0.103409	+	0.0244214i
$253$	4.47833	+	7.75669i	0.281550	+	0.487659i
$254$	−3.57207	−	6.18701i	−0.224132	−	0.388208i
$255$	1.14381	+	9.81992i	0.0716284	+	0.614947i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.24025	+	5.61228i	−0.202121	+	0.350084i	−0.949212	−	0.314638i	$-0.898117\pi$
$257$	−3.24025	+	5.61228i	−0.202121	+	0.350084i	0.747090	+	0.664722i	$0.231450\pi$
$258$	−18.6859	−	8.06915i	−1.16333	−	0.502363i
$259$	−2.05628			−0.127771
$260$	2.03006	−	3.51617i	0.125899	−	0.218064i
$261$	12.5157	−	2.95574i	0.774703	−	0.182955i
$262$	−1.74226	+	3.01768i	−0.107637	+	0.186433i
$263$	7.90071	−	13.6844i	0.487178	−	0.843818i	−0.512713	−	0.858560i	$-0.671359\pi$
$263$	7.90071	−	13.6844i	0.487178	−	0.843818i	0.999891	+	0.0147424i	$0.00469283\pi$
$264$	6.34754	+	2.74107i	0.390664	+	0.168701i
$265$	−4.04109			−0.248242
$266$	0.818166	−	1.41711i	0.0501650	−	0.0868883i
$267$	5.78462	+	2.49798i	0.354013	+	0.152874i
$268$	5.68951			0.347542
$269$	−5.24517	−	9.08490i	−0.319804	−	0.553916i	0.660643	−	0.750700i	$-0.270284\pi$
$269$	−5.24517	−	9.08490i	−0.319804	−	0.553916i	−0.980447	+	0.196784i	$0.936950\pi$
$270$	−9.23590	+	10.9802i	−0.562079	+	0.668234i
$271$	19.1276			1.16192			0.580959	−	0.813933i	$-0.302678\pi$
$271$	19.1276			1.16192			0.580959	+	0.813933i	$0.302678\pi$
$272$	−1.03355	−	1.79016i	−0.0626683	−	0.108545i
$273$	1.31457	+	0.567671i	0.0795613	+	0.0343570i
$274$	−0.834449	+	1.44531i	−0.0504109	+	0.0873143i
$275$	5.23871	+	9.07371i	0.315906	+	0.547165i
$276$	3.11818	−	2.31947i	0.187692	−	0.139616i
$277$	−2.65245	+	4.59418i	−0.159370	+	0.276038i	−0.934642	−	0.355591i	$-0.884280\pi$
$277$	−2.65245	+	4.59418i	−0.159370	+	0.276038i	0.775271	+	0.631628i	$0.217613\pi$
$278$	16.5616			0.993296
$279$	16.6853	−	0.776115i	0.998920	−	0.0464648i
$280$	1.55251			0.0927804
$281$	11.3592	−	19.6748i	0.677635	−	1.17370i	−0.298057	−	0.954548i	$-0.596338\pi$
$281$	11.3592	−	19.6748i	0.677635	−	1.17370i	0.975691	−	0.219149i	$-0.0703282\pi$
$282$	−1.18974	−	10.2142i	−0.0708479	−	0.608247i
$283$	12.8023	+	22.1743i	0.761019	+	1.31812i	0.942326	+	0.334697i	$0.108634\pi$
$283$	12.8023	+	22.1743i	0.761019	+	1.31812i	−0.181307	+	0.983427i	$0.558033\pi$
$284$	2.14830	−	3.72096i	0.127478	−	0.220798i
$285$	−1.61043	−	13.8259i	−0.0953934	−	0.818975i
$286$	−2.93476	−	5.08316i	−0.173536	−	0.300573i
$287$	−3.50755			−0.207044
$288$	0.862702	−	2.87328i	0.0508352	−	0.169310i
$289$	6.36354	+	11.0220i	0.374326	+	0.648351i
$290$	−11.8367			−0.695076
$291$	22.0941	−	16.4348i	1.29518	−	0.963424i
$292$	−4.67244	+	8.09290i	−0.273434	+	0.473601i
$293$	−6.34563			−0.370715			−0.185358	−	0.982671i	$-0.559344\pi$
$293$	−6.34563			−0.370715			−0.185358	+	0.982671i	$0.559344\pi$
$294$	−1.33940	−	11.4991i	−0.0781154	−	0.670640i
$295$	1.75512	−	3.03996i	0.102187	−	0.176993i
$296$	1.82864	−	3.16730i	0.106288	−	0.184096i
$297$	7.07095	+	19.4999i	0.410298	+	1.13150i
$298$	6.37166	−	11.0360i	0.369101	−	0.639301i
$299$	−3.29913			−0.190793
$300$	3.64762	−	2.71329i	0.210596	−	0.156652i
$301$	−3.30352	+	5.72187i	−0.190412	+	0.329803i
$302$	−2.16532	−	3.75045i	−0.124600	−	0.215814i
$303$	−2.92980	+	2.17934i	−0.168313	+	0.125200i
$304$	1.45518	+	2.52045i	0.0834605	+	0.144558i
$305$	−19.1159	−	33.1097i	−1.09457	−	1.89586i
$306$	1.78330	−	5.93937i	0.101944	−	0.339531i
$307$	2.68363	−	4.64819i	0.153163	−	0.265286i	−0.779226	−	0.626743i	$-0.784387\pi$
$307$	2.68363	−	4.64819i	0.153163	−	0.265286i	0.932389	+	0.361457i	$0.117721\pi$
$308$	1.12220	−	1.94370i	0.0639431	−	0.110753i
$309$	−16.3787	+	12.1833i	−0.931750	+	0.693084i
$310$	−15.1106	−	2.83455i	−0.858226	−	0.160991i
$311$	−14.3458	−	24.8477i	−0.813476	−	1.40898i	−0.910417	−	0.413691i	$-0.864239\pi$
$311$	−14.3458	−	24.8477i	−0.813476	−	1.40898i	0.0969413	−	0.995290i	$-0.469094\pi$
$312$	−2.04343	+	1.52001i	−0.115686	+	0.0860535i
$313$	−3.51471	−	6.08766i	−0.198663	−	0.344095i	0.749432	−	0.662081i	$-0.230327\pi$
$313$	−3.51471	−	6.08766i	−0.198663	−	0.344095i	−0.948095	+	0.317986i	$0.896993\pi$
$314$	22.1618			1.25066
$315$	3.19349	+	3.39032i	0.179933	+	0.191023i
$316$	0.516125	−	0.893955i	0.0290343	−	0.0502889i
$317$	−2.92859	−	5.07247i	−0.164486	−	0.284898i	0.771987	−	0.635639i	$-0.219263\pi$
$317$	−2.92859	−	5.07247i	−0.164486	−	0.284898i	−0.936473	+	0.350741i	$0.885930\pi$
$318$	2.32711	+	1.00492i	0.130498	+	0.0563531i
$319$	−8.55588	+	14.8192i	−0.479037	+	0.829717i
$320$	−1.38064	+	2.39134i	−0.0771803	+	0.133680i
$321$	8.52862	−	6.34404i	0.476021	−	0.354090i
$322$	−0.630761	−	1.09251i	−0.0351509	−	0.0608832i
$323$	3.00802	+	5.21004i	0.167370	+	0.289894i
$324$	8.04913	−	4.02636i	0.447174	−	0.223686i
$325$	−3.85929			−0.214075
$326$	−0.911611	+	1.57896i	−0.0504895	+	0.0874503i
$327$	−20.4558	−	8.83346i	−1.13121	−	0.488492i
$328$	3.11925	−	5.40270i	0.172232	−	0.298314i
$329$	−3.33806			−0.184033
$330$	−2.20886	−	18.9636i	−0.121594	−	1.04391i
$331$	−14.4242			−0.792828			−0.396414	−	0.918072i	$-0.629745\pi$
$331$	−14.4242			−0.792828			−0.396414	+	0.918072i	$0.629745\pi$
$332$	1.02216	+	1.77044i	0.0560986	+	0.0971656i
$333$	10.6781	−	2.52176i	0.585157	−	0.138192i
$334$	3.20854	−	5.55736i	0.175564	−	0.304085i
$335$	−7.85518	−	13.6056i	−0.429175	−	0.743352i
$336$	−0.894036	−	0.386072i	−0.0487736	−	0.0210620i
$337$	13.7311	+	23.7829i	0.747978	+	1.29554i	0.948790	+	0.315907i	$0.102309\pi$
$337$	13.7311	+	23.7829i	0.747978	+	1.29554i	−0.200812	+	0.979630i	$0.564358\pi$
$338$	−10.8380			−0.589509
$339$	−19.0668	+	14.1829i	−1.03556	+	0.770308i
$340$	−2.85393	+	4.94316i	−0.154776	+	0.268080i
$341$	−14.4711	+	16.8692i	−0.783655	+	0.913517i
$342$	−2.51078	+	8.36230i	−0.135767	+	0.452181i
$343$	−7.69367			−0.415419
$344$	−5.87561	−	10.1769i	−0.316792	−	0.548700i
$345$	−9.85174	−	4.25429i	−0.530400	−	0.229043i
$346$	10.5109	−	18.2054i	0.565068	−	0.978726i
$347$	−9.86345			−0.529498			−0.264749	−	0.964317i	$-0.585289\pi$
$347$	−9.86345			−0.529498			−0.264749	+	0.964317i	$0.585289\pi$
$348$	6.81633	+	2.94350i	0.365393	+	0.157788i
$349$	5.34850	−	9.26388i	0.286299	−	0.495884i	−0.686624	−	0.727012i	$-0.740908\pi$
$349$	5.34850	−	9.26388i	0.286299	−	0.495884i	0.972923	+	0.231128i	$0.0742417\pi$
$350$	−0.737859	−	1.27801i	−0.0394402	−	0.0683125i
$351$	−7.52263	−	1.33573i	−0.401528	−	0.0712958i
$352$	1.99593	+	3.45705i	0.106383	+	0.184261i
$353$	−14.5379	−	25.1803i	−0.773773	−	1.34021i	−0.935481	−	0.353376i	$-0.885034\pi$
$353$	−14.5379	−	25.1803i	−0.773773	−	1.34021i	0.161708	−	0.986839i	$-0.448300\pi$
$354$	−1.76667	+	1.31414i	−0.0938976	+	0.0698460i
$355$	−11.8641			−0.629682
$356$	1.81892	+	3.15047i	0.0964027	+	0.166974i
$357$	−1.84807	−	0.798052i	−0.0978100	−	0.0422374i
$358$	7.59632	+	13.1572i	0.401478	+	0.695380i
$359$	1.79467	+	3.10846i	0.0947189	+	0.164058i	0.909491	−	0.415723i	$-0.136471\pi$
$359$	1.79467	+	3.10846i	0.0947189	+	0.164058i	−0.814772	+	0.579781i	$0.803138\pi$
$360$	−8.06209	+	1.90396i	−0.424909	+	0.100347i
$361$	5.26489	+	9.11905i	0.277099	+	0.479950i
$362$	2.75534			0.144817
$363$	−7.84712	−	3.38863i	−0.411867	−	0.177857i
$364$	0.413354	+	0.715950i	0.0216656	+	0.0375260i
$365$	25.8039			1.35064
$366$	2.77457	+	23.8203i	0.145029	+	1.24511i
$367$	−14.6889			−0.766754			−0.383377	−	0.923592i	$-0.625239\pi$
$367$	−14.6889			−0.766754			−0.383377	+	0.923592i	$0.625239\pi$
$368$	2.24373			0.116963
$369$	18.2144	−	4.30156i	0.948206	−	0.223930i
$370$	−10.0988			−0.525012
$371$	0.411416	−	0.712593i	0.0213596	−	0.0369960i
$372$	7.99677	+	5.38996i	0.414613	+	0.279456i
$373$	−19.2242	−	33.2973i	−0.995392	−	1.72407i	−0.580741	−	0.814088i	$-0.697237\pi$
$373$	−19.2242	−	33.2973i	−0.995392	−	1.72407i	−0.414651	−	0.909981i	$-0.636096\pi$
$374$	4.12579	+	7.14608i	0.213340	+	0.369515i
$375$	10.4294	+	4.50375i	0.538574	+	0.232573i
$376$	2.96852	−	5.14163i	0.153090	−	0.265159i
$377$	−3.15150	−	5.45856i	−0.162311	−	0.281130i
$378$	−0.995926	−	2.74651i	−0.0512249	−	0.141265i
$379$	−13.8582	+	24.0031i	−0.711849	+	1.23296i	0.252313	+	0.967646i	$0.418809\pi$
$379$	−13.8582	+	24.0031i	−0.711849	+	1.23296i	−0.964162	+	0.265313i	$0.914525\pi$
$380$	4.01818	−	6.95968i	0.206128	−	0.357024i
$381$	9.92844	−	7.38529i	0.508649	−	0.378360i
$382$	−8.80426	+	15.2494i	−0.450465	+	0.780229i
$383$	−11.0303	+	19.1051i	−0.563624	+	0.976225i	0.433552	+	0.901128i	$0.357260\pi$
$383$	−11.0303	+	19.1051i	−0.563624	+	0.976225i	−0.997176	+	0.0750969i	$0.976073\pi$
$384$	1.38973	−	1.03375i	0.0709194	−	0.0527536i
$385$	−6.19741			−0.315849
$386$	−2.11290	+	3.65965i	−0.107544	+	0.186272i
$387$	10.1378	−	33.7646i	0.515334	−	1.71635i
$388$	15.8981			0.807106
$389$	1.37490	+	2.38140i	0.0697103	+	0.120742i	0.898774	−	0.438413i	$-0.144459\pi$
$389$	1.37490	+	2.38140i	0.0697103	+	0.120742i	−0.829063	+	0.559154i	$0.811126\pi$
$390$	6.45610	+	2.78794i	0.326917	+	0.141173i
$391$	4.63803			0.234555
$392$	3.34194	−	5.78841i	0.168794	−	0.292359i
$393$	−5.54081	−	2.39269i	−0.279497	−	0.120695i
$394$	22.1097			1.11387
$395$	−2.85034			−0.143416
$396$	−3.44378	+	11.4697i	−0.173057	+	0.576375i
$397$	−0.820424	+	1.42102i	−0.0411759	+	0.0713187i	−0.885879	−	0.463917i	$-0.846444\pi$
$397$	−0.820424	+	1.42102i	−0.0411759	+	0.0713187i	0.844703	+	0.535235i	$0.179777\pi$
$398$	8.45190			0.423656
$399$	2.60197	+	1.12361i	0.130261	+	0.0562510i
$400$	2.62470			0.131235
$401$	−4.89561	−	8.47944i	−0.244475	−	0.423443i	0.717509	−	0.696549i	$-0.245282\pi$
$401$	−4.89561	−	8.47944i	−0.244475	−	0.423443i	−0.961984	+	0.273106i	$0.911949\pi$
$402$	1.14014	+	9.78835i	0.0568648	+	0.488198i
$403$	−2.71601	−	7.72304i	−0.135294	−	0.384712i
$404$	−2.10818			−0.104886
$405$	−20.7414	−	13.6893i	−1.03065	−	0.680225i
$406$	1.20507	−	2.08725i	0.0598068	−	0.103588i
$407$	−7.29967	+	12.6434i	−0.361831	+	0.626710i
$408$	2.87272	−	2.13688i	0.142221	−	0.105791i
$409$	16.7776			0.829599			0.414799	−	0.909913i	$-0.363852\pi$
$409$	16.7776			0.829599			0.414799	+	0.909913i	$0.363852\pi$
$410$	−17.2263			−0.850745
$411$	−2.65375	−	1.14597i	−0.130900	−	0.0565267i
$412$	−11.7855			−0.580630
$413$	0.357371	+	0.618985i	0.0175851	+	0.0304583i
$414$	4.61532	+	4.89978i	0.226831	+	0.240811i
$415$	2.82249	−	4.88869i	0.138551	−	0.239977i
$416$	−1.47038			−0.0720911
$417$	3.31881	+	28.4928i	0.162523	+	1.39530i
$418$	−5.80888	−	10.0613i	−0.284122	−	0.492113i
$419$	11.7683	+	20.3833i	0.574919	+	0.995789i	0.996050	+	0.0887895i	$0.0282998\pi$
$419$	11.7683	+	20.3833i	0.574919	+	0.995789i	−0.421131	+	0.907000i	$0.638367\pi$
$420$	0.311112	+	2.67097i	0.0151807	+	0.130330i
$421$	35.4521			1.72783			0.863915	−	0.503638i	$-0.168005\pi$
$421$	35.4521			1.72783			0.863915	+	0.503638i	$0.168005\pi$
$422$	−13.3678	+	23.1538i	−0.650736	+	1.12711i
$423$	17.3343	−	4.09370i	0.842822	−	0.199042i
$424$	0.731740	+	1.26741i	0.0355364	+	0.0615509i
$425$	5.42553			0.263177
$426$	6.83211	+	2.95032i	0.331017	+	0.142943i
$427$	7.78463			0.376724
$428$	6.13689			0.296638
$429$	8.15706	−	6.06765i	0.393827	−	0.292949i
$430$	−16.2242	+	28.1012i	−0.782403	+	1.35516i
$431$	−10.4796	+	18.1512i	−0.504785	+	0.874314i	0.495199	+	0.868779i	$0.335095\pi$
$431$	−10.4796	+	18.1512i	−0.504785	+	0.874314i	−0.999985	+	0.00553455i	$0.998238\pi$
$432$	5.11613	+	0.908425i	0.246150	+	0.0437066i
$433$	−6.09639			−0.292974			−0.146487	−	0.989213i	$-0.546797\pi$
$433$	−6.09639			−0.292974			−0.146487	+	0.989213i	$0.546797\pi$
$434$	2.03822	−	2.37598i	0.0978377	−	0.114051i
$435$	−2.37199	−	20.3641i	−0.113728	−	0.976384i
$436$	−6.43215	−	11.1408i	−0.308044	−	0.533548i
$437$	−6.53008			−0.312376
$438$	−14.8595	−	6.41680i	−0.710015	−	0.306606i
$439$	−27.7751			−1.32563			−0.662817	−	0.748781i	$-0.730639\pi$
$439$	−27.7751			−1.32563			−0.662817	+	0.748781i	$0.730639\pi$
$440$	5.51133	−	9.54590i	0.262742	−	0.455083i
$441$	19.5148	−	4.60866i	0.929278	−	0.219460i
$442$	−3.03942			−0.144570
$443$	3.02353			0.143652			0.0718262	−	0.997417i	$-0.477117\pi$
$443$	3.02353			0.143652			0.0718262	+	0.997417i	$0.477117\pi$
$444$	5.81553	+	2.51133i	0.275993	+	0.119182i
$445$	5.02257	−	8.69934i	0.238092	−	0.412388i
$446$	21.2515			1.00629
$447$	20.2635	+	8.75039i	0.958429	+	0.413879i
$448$	−0.281122	−	0.486917i	−0.0132817	−	0.0230047i
$449$	−26.6291			−1.25671			−0.628353	−	0.777928i	$-0.716271\pi$
$449$	−26.6291			−1.25671			−0.628353	+	0.777928i	$0.716271\pi$
$450$	5.39896	+	5.73172i	0.254509	+	0.270196i
$451$	−12.4516	+	21.5668i	−0.586322	+	1.01554i
$452$	−13.7198			−0.645323
$453$	6.01843	−	4.47683i	0.282771	−	0.210340i
$454$	13.2692	−	22.9830i	0.622756	−	1.07865i
$455$	1.14139	−	1.97694i	0.0535091	−	0.0926805i
$456$	−4.04462	+	3.00860i	−0.189407	+	0.140891i
$457$	6.35410	−	11.0056i	0.297232	−	0.514822i	−0.678269	−	0.734813i	$-0.737270\pi$
$457$	6.35410	−	11.0056i	0.297232	−	0.514822i	0.975502	+	0.219992i	$0.0706030\pi$
$458$	1.01441	−	1.75702i	0.0474005	−	0.0821000i
$459$	10.5756	+	1.87781i	0.493625	+	0.0876487i
$460$	−3.09779	−	5.36553i	−0.144435	−	0.250169i
$461$	10.5442	−	18.2631i	0.491093	−	0.850597i	−0.508855	−	0.860852i	$-0.669931\pi$
$461$	10.5442	−	18.2631i	0.491093	−	0.850597i	0.999947	+	0.0102549i	$0.00326431\pi$
$462$	3.56886	+	1.54115i	0.166038	+	0.0717006i
$463$	−8.33955	−	14.4445i	−0.387572	−	0.671294i	0.604551	−	0.796567i	$-0.293353\pi$
$463$	−8.33955	−	14.4445i	−0.387572	−	0.671294i	−0.992122	+	0.125273i	$0.960019\pi$
$464$	2.14333	+	3.71236i	0.0995017	+	0.172342i
$465$	1.84855	−	26.5646i	0.0857244	−	1.23191i
$466$	−6.47283	+	11.2113i	−0.299848	+	0.519352i
$467$	−34.4397			−1.59368			−0.796840	−	0.604191i	$-0.793496\pi$
$467$	−34.4397			−1.59368			−0.796840	+	0.604191i	$0.793496\pi$
$468$	−3.02454	−	3.21095i	−0.139809	−	0.148426i
$469$	3.19889			0.147711
$470$	−16.3939			−0.756193
$471$	4.44106	+	38.1276i	0.204633	+	1.75683i
$472$	−1.27123			−0.0585133
$473$	23.4546	+	40.6246i	1.07844	+	1.86792i
$474$	1.64140	+	0.708809i	0.0753922	+	0.0325567i
$475$	−7.63883			−0.350494
$476$	−0.581108	−	1.00651i	−0.0266350	−	0.0461332i
$477$	−1.26255	+	4.20499i	−0.0578081	+	0.192533i
$478$	−6.91699	−	11.9806i	−0.316376	−	0.547979i
$479$	−12.6337	−	21.8823i	−0.577250	−	0.999826i	−0.995793	−	0.0916290i	$-0.970793\pi$
$479$	−12.6337	−	21.8823i	−0.577250	−	0.999826i	0.418544	−	0.908197i	$-0.362541\pi$
$480$	−4.39078	−	1.89608i	−0.200411	−	0.0865437i
$481$	−2.68879	−	4.65712i	−0.122598	−	0.212346i
$482$	−27.8602			−1.26900
$483$	1.75318	−	1.30410i	0.0797723	−	0.0593388i
$484$	−2.46746	−	4.27376i	−0.112157	−	0.194262i
$485$	−21.9497	−	38.0179i	−0.996683	−	1.72630i
$486$	8.54000	+	13.0410i	0.387382	+	0.591553i
$487$	−13.9395	−	24.1440i	−0.631660	−	1.09407i	−0.987212	−	0.159411i	$-0.949040\pi$
$487$	−13.9395	−	24.1440i	−0.631660	−	1.09407i	0.355552	−	0.934657i	$-0.384293\pi$
$488$	−6.92283	+	11.9907i	−0.313382	+	0.542793i
$489$	−2.89915	−	1.25194i	−0.131104	−	0.0566148i
$490$	−18.4561			−0.833762
$491$	−1.00378	+	1.73860i	−0.0452999	+	0.0784618i	−0.887786	−	0.460256i	$-0.847758\pi$
$491$	−1.00378	+	1.73860i	−0.0452999	+	0.0784618i	0.842486	+	0.538718i	$0.181091\pi$
$492$	9.91998	+	4.28375i	0.447227	+	0.193127i
$493$	4.43049	+	7.67384i	0.199539	+	0.345612i
$494$	4.27933			0.192536
$495$	32.1827	−	7.60033i	1.44650	−	0.341609i
$496$	1.84716	+	5.25243i	0.0829397	+	0.235841i
$497$	1.20786	−	2.09208i	0.0541801	−	0.0938427i
$498$	−2.84107	+	2.11334i	−0.127311	+	0.0947008i
$499$	−20.5227			−0.918720			−0.459360	−	0.888250i	$-0.651921\pi$
$499$	−20.5227			−0.918720			−0.459360	+	0.888250i	$0.651921\pi$
$500$	3.27944	+	5.68016i	0.146661	+	0.254025i
$501$	10.2040	+	4.40639i	0.455879	+	0.196863i
$502$	4.36267	+	7.55637i	0.194716	+	0.337257i
$503$	−16.3446	+	28.3097i	−0.728771	+	1.26227i	0.228632	+	0.973513i	$0.426575\pi$
$503$	−16.3446	+	28.3097i	−0.728771	+	1.26227i	−0.957403	+	0.288755i	$0.906759\pi$
$504$	0.485048	−	1.61548i	0.0216058	−	0.0719593i
$505$	2.91064	+	5.04138i	0.129522	+	0.224339i
$506$	−8.95665			−0.398172
$507$	−2.17185	−	18.6459i	−0.0964554	−	0.828094i
$508$	7.14415			0.316970
$509$	−15.4177	+	26.7042i	−0.683376	+	1.18364i	0.290568	+	0.956854i	$0.406156\pi$
$509$	−15.4177	+	26.7042i	−0.683376	+	1.18364i	−0.973944	+	0.226788i	$0.927178\pi$
$510$	−9.07621	−	3.91939i	−0.401901	−	0.173553i
$511$	−2.62705	+	4.55018i	−0.116214	+	0.201288i
$512$	1.00000			0.0441942
$513$	−14.8898	−	2.64385i	−0.657401	−	0.116729i
$514$	−3.24025	−	5.61228i	−0.142921	−	0.247547i
$515$	16.2716	+	28.1832i	0.717011	+	1.24190i
$516$	16.3310	−	12.1479i	0.718934	−	0.534781i
$517$	−11.8499	+	20.5246i	−0.521158	+	0.902673i
$518$	1.02814	−	1.78079i	0.0451739	−	0.0782435i
$519$	33.4272	+	14.4349i	1.46729	+	0.633621i
$520$	2.03006	+	3.51617i	0.0890241	+	0.154194i
$521$	4.71147	−	8.16051i	0.206413	−	0.357519i	−0.744169	−	0.667992i	$-0.767154\pi$
$521$	4.71147	−	8.16051i	0.206413	−	0.357519i	0.950582	+	0.310473i	$0.100487\pi$
$522$	−3.69812	+	12.3168i	−0.161862	+	0.539092i
$523$	40.0302			1.75040			0.875200	−	0.483761i	$-0.160730\pi$
$523$	40.0302			1.75040			0.875200	+	0.483761i	$0.160730\pi$
$524$	−1.74226	−	3.01768i	−0.0761109	−	0.131828i
$525$	2.05085	−	1.52553i	0.0895065	−	0.0665796i
$526$	7.90071	+	13.6844i	0.344487	+	0.596669i
$527$	3.81826	+	10.8573i	0.166326	+	0.472952i
$528$	−5.54760	+	4.12660i	−0.241429	+	0.179587i
$529$	8.98284	−	15.5587i	0.390558	−	0.676466i
$530$	2.02054	−	3.49968i	0.0877668	−	0.152016i
$531$	−2.61491	−	2.77607i	−0.113477	−	0.120471i
$532$	0.818166	+	1.41711i	0.0354720	+	0.0614393i
$533$	−4.58646	−	7.94399i	−0.198662	−	0.344092i
$534$	−5.05563	+	3.76064i	−0.218778	+	0.162739i
$535$	−8.47285	−	14.6754i	−0.366313	−	0.634473i
$536$	−2.84476	+	4.92726i	−0.122875	+	0.212825i
$537$	−21.1137	+	15.7055i	−0.911122	+	0.677740i
$538$	10.4903			0.452271
$539$	−13.3405	+	23.1065i	−0.574618	+	0.995268i
$540$	−4.89119	−	13.4886i	−0.210483	−	0.580458i
$541$	−7.70912	+	13.3526i	−0.331441	+	0.574073i	−0.982795	−	0.184702i	$-0.940868\pi$
$541$	−7.70912	+	13.3526i	−0.331441	+	0.574073i	0.651354	+	0.758774i	$0.274201\pi$
$542$	−9.56379	+	16.5650i	−0.410800	+	0.711527i
$543$	0.552149	+	4.74034i	0.0236950	+	0.203427i
$544$	2.06710			0.0886264
$545$	−17.7610	+	30.7630i	−0.760798	+	1.31774i
$546$	−1.14890	+	0.854613i	−0.0491684	+	0.0365741i
$547$	−5.40646			−0.231164			−0.115582	−	0.993298i	$-0.536873\pi$
$547$	−5.40646			−0.231164			−0.115582	+	0.993298i	$0.536873\pi$
$548$	−0.834449	−	1.44531i	−0.0356459	−	0.0617405i
$549$	−40.4250	+	9.54684i	−1.72530	+	0.407449i
$550$	−10.4774			−0.446759
$551$	−6.23788	−	10.8043i	−0.265743	−	0.460280i
$552$	0.449627	+	3.86016i	0.0191374	+	0.164299i
$553$	0.290188	−	0.502620i	0.0123400	−	0.0213736i
$554$	−2.65245	−	4.59418i	−0.112692	−	0.195188i
$555$	−2.02373	−	17.3742i	−0.0859024	−	0.737493i
$556$	−8.28078	+	14.3427i	−0.351183	+	0.608267i
$557$	27.1620			1.15089			0.575445	−	0.817840i	$-0.304829\pi$
$557$	27.1620			1.15089			0.575445	+	0.817840i	$0.304829\pi$
$558$	−7.67049	+	14.8379i	−0.324718	+	0.628139i
$559$	−17.2787			−0.730812
$560$	−0.776257	+	1.34452i	−0.0328028	+	0.0568162i
$561$	−11.4675	+	8.53011i	−0.484157	+	0.360142i
$562$	11.3592	+	19.6748i	0.479160	+	0.829929i
$563$	−2.45043	+	4.24427i	−0.103273	+	0.178874i	−0.913031	−	0.407889i	$-0.866265\pi$
$563$	−2.45043	+	4.24427i	−0.103273	+	0.178874i	0.809758	+	0.586764i	$0.199598\pi$
$564$	9.44063	+	4.07676i	0.397522	+	0.171662i
$565$	18.9421	+	32.8087i	0.796900	+	1.38027i
$566$	−25.6046			−1.07624
$567$	4.52557	−	2.26379i	0.190056	−	0.0950702i
$568$	2.14830	+	3.72096i	0.0901405	+	0.156128i
$569$	26.8565			1.12589			0.562943	−	0.826496i	$-0.309669\pi$
$569$	26.8565			1.12589			0.562943	+	0.826496i	$0.309669\pi$
$570$	12.7788	+	5.51828i	0.535245	+	0.231135i
$571$	−19.4371	+	33.6661i	−0.813419	+	1.40888i	0.0970391	+	0.995281i	$0.469063\pi$
$571$	−19.4371	+	33.6661i	−0.813419	+	1.40888i	−0.910458	+	0.413602i	$0.864271\pi$
$572$	5.86953			0.245417
$573$	−27.9997	−	12.0911i	−1.16971	−	0.505115i
$574$	1.75378	−	3.03763i	0.0732012	−	0.126788i
$575$	−2.94456	+	5.10013i	−0.122797	+	0.212690i
$576$	2.05698	+	2.18376i	0.0857076	+	0.0909901i
$577$	3.68743	−	6.38682i	0.153510	−	0.265887i	−0.779006	−	0.627017i	$-0.784276\pi$
$577$	3.68743	−	6.38682i	0.153510	−	0.265887i	0.932515	+	0.361130i	$0.117609\pi$
$578$	−12.7271			−0.529377
$579$	−6.71955	−	2.90171i	−0.279255	−	0.120591i
$580$	5.91835	−	10.2509i	0.245746	−	0.425645i
$581$	0.574705	+	0.995418i	0.0238428	+	0.0412969i
$582$	3.18587	+	27.3515i	0.132059	+	1.13376i
$583$	−2.92100	−	5.05932i	−0.120975	−	0.209536i
$584$	−4.67244	−	8.09290i	−0.193347	−	0.334887i
$585$	−3.50268	+	11.6659i	−0.144818	+	0.482325i
$586$	3.17281	−	5.49547i	0.131068	−	0.227016i
$587$	17.2870	−	29.9420i	0.713511	−	1.23584i	−0.250019	−	0.968241i	$-0.580437\pi$
$587$	17.2870	−	29.9420i	0.713511	−	1.23584i	0.963531	−	0.267597i	$-0.0862297\pi$
$588$	10.6282	+	4.58959i	0.438299	+	0.189271i
$589$	−5.37590	−	15.2865i	−0.221510	−	0.629869i
$590$	1.75512	+	3.03996i	0.0722571	+	0.125153i
$591$	4.43061	+	38.0379i	0.182251	+	1.56467i
$592$	1.82864	+	3.16730i	0.0751567	+	0.130175i
$593$	20.4038			0.837884			0.418942	−	0.908013i	$-0.362401\pi$
$593$	20.4038			0.837884			0.418942	+	0.908013i	$0.362401\pi$
$594$	−20.4228	−	3.62630i	−0.837960	−	0.148789i
$595$	−1.60460	+	2.77926i	−0.0657823	+	0.113938i
$596$	6.37166	+	11.0360i	0.260994	+	0.452054i
$597$	1.69370	+	14.5408i	0.0693185	+	0.595116i
$598$	1.64956	−	2.85713i	0.0674557	−	0.116837i
$599$	18.7854	−	32.5373i	0.767551	−	1.32944i	−0.171337	−	0.985213i	$-0.554809\pi$
$599$	18.7854	−	32.5373i	0.767551	−	1.32944i	0.938887	−	0.344224i	$-0.111858\pi$
$600$	0.525970	+	4.51558i	0.0214726	+	0.184348i
$601$	−7.88826	−	13.6629i	−0.321769	−	0.557320i	0.659084	−	0.752069i	$-0.270944\pi$
$601$	−7.88826	−	13.6629i	−0.321769	−	0.557320i	−0.980853	+	0.194749i	$0.937611\pi$
$602$	−3.30352	−	5.72187i	−0.134642	−	0.233206i
$603$	−16.6116	+	3.92302i	−0.676476	+	0.159758i
$604$	4.33065			0.176212
$605$	−6.81336	+	11.8011i	−0.277002	+	0.479782i
$606$	−0.422464	−	3.62695i	−0.0171614	−	0.147335i
$607$	−3.23359	+	5.60074i	−0.131247	+	0.227327i	−0.924158	−	0.382011i	$-0.875232\pi$
$607$	−3.23359	+	5.60074i	−0.131247	+	0.227327i	0.792910	+	0.609338i	$0.208565\pi$
$608$	−2.91037			−0.118031
$609$	3.83243	+	1.65496i	0.155298	+	0.0670625i
$610$	38.2318			1.54796
$611$	−4.36484	−	7.56012i	−0.176582	−	0.305850i
$612$	4.25200	+	4.51407i	0.171877	+	0.182470i
$613$	−9.79127	+	16.9590i	−0.395466	+	0.684967i	−0.993160	−	0.116757i	$-0.962750\pi$
$613$	−9.79127	+	16.9590i	−0.395466	+	0.684967i	0.597695	+	0.801724i	$0.296083\pi$
$614$	2.68363	+	4.64819i	0.108303	+	0.187586i
$615$	−3.45202	−	29.6364i	−0.139199	−	1.19506i
$616$	1.12220	+	1.94370i	0.0452146	+	0.0783140i
$617$	10.6772			0.429846			0.214923	−	0.976631i	$-0.431050\pi$
$617$	10.6772			0.429846			0.214923	+	0.976631i	$0.431050\pi$
$618$	−2.36173	−	20.2760i	−0.0950026	−	0.815620i
$619$	4.27984	−	7.41290i	0.172021	−	0.297950i	−0.767105	−	0.641521i	$-0.778304\pi$
$619$	4.27984	−	7.41290i	0.172021	−	0.297950i	0.939126	+	0.343572i	$0.111637\pi$
$620$	10.0101	−	11.6689i	0.402015	−	0.468635i
$621$	−7.50479	+	8.92216i	−0.301157	+	0.358034i
$622$	28.6916			1.15043
$623$	1.02268	+	1.77133i	0.0409727	+	0.0709668i
$624$	−0.294652	−	2.52966i	−0.0117955	−	0.101268i
$625$	15.6172	−	27.0498i	0.624689	−	1.08199i
$626$	7.02943			0.280953
$627$	16.1456	−	12.0099i	0.644792	−	0.479630i
$628$	−11.0809	+	19.1927i	−0.442176	+	0.765872i
$629$	3.77999	+	6.54714i	0.150718	+	0.261052i
$630$	−4.53285	+	1.07049i	−0.180593	+	0.0426492i
$631$	−8.95079	−	15.5032i	−0.356325	−	0.617174i	0.631018	−	0.775768i	$-0.282637\pi$
$631$	−8.95079	−	15.5032i	−0.356325	−	0.617174i	−0.987344	+	0.158594i	$0.949304\pi$
$632$	0.516125	+	0.893955i	0.0205303	+	0.0355596i
$633$	−42.5130	−	18.3584i	−1.68974	−	0.729682i
$634$	5.85718			0.232619
$635$	−9.86351	−	17.0841i	−0.391422	−	0.677962i
$636$	−2.03384	+	1.51288i	−0.0806471	+	0.0599896i
$637$	−4.91391	−	8.51114i	−0.194696	−	0.337224i
$638$	−8.55588	−	14.8192i	−0.338730	−	0.586698i
$639$	−3.70668	+	12.3453i	−0.146634	+	0.488373i
$640$	−1.38064	−	2.39134i	−0.0545747	−	0.0945262i
$641$	−1.27105			−0.0502034			−0.0251017	−	0.999685i	$-0.507991\pi$
$641$	−1.27105			−0.0502034			−0.0251017	+	0.999685i	$0.507991\pi$
$642$	1.22979	+	10.5580i	0.0485358	+	0.416692i
$643$	21.4808	+	37.2058i	0.847119	+	1.46725i	0.883769	+	0.467924i	$0.154998\pi$
$643$	21.4808	+	37.2058i	0.847119	+	1.46725i	−0.0366500	+	0.999328i	$0.511669\pi$
$644$	1.26152			0.0497109
$645$	−51.5971	−	22.2812i	−2.03163	−	0.877323i
$646$	−6.01603			−0.236698
$647$	31.9389			1.25565			0.627824	−	0.778355i	$-0.283946\pi$
$647$	31.9389			1.25565			0.627824	+	0.778355i	$0.283946\pi$
$648$	−0.537638	+	8.98393i	−0.0211204	+	0.352922i
$649$	5.07458			0.199195
$650$	1.92965	−	3.34224i	0.0756869	−	0.131094i
$651$	4.49613	+	3.03047i	0.176217	+	0.118773i
$652$	−0.911611	−	1.57896i	−0.0357014	−	0.0618367i
$653$	1.74521	+	3.02279i	0.0682953	+	0.118291i	0.898151	−	0.439687i	$-0.144911\pi$
$653$	1.74521	+	3.02279i	0.0682953	+	0.118291i	−0.829856	+	0.557978i	$0.811577\pi$
$654$	17.8779	−	13.2985i	0.699082	−	0.520014i
$655$	−4.81087	+	8.33268i	−0.187976	+	0.325585i
$656$	3.11925	+	5.40270i	0.121786	+	0.210940i
$657$	8.06185	−	26.8505i	0.314523	−	1.04754i
$658$	1.66903	−	2.89084i	0.0650656	−	0.112697i
$659$	−5.41504	+	9.37912i	−0.210940	+	0.365359i	−0.952009	−	0.306070i	$-0.900986\pi$
$659$	−5.41504	+	9.37912i	−0.210940	+	0.365359i	0.741069	+	0.671429i	$0.234319\pi$
$660$	17.5274	+	7.56887i	0.682252	+	0.294618i
$661$	14.6983	−	25.4582i	0.571698	−	0.990209i	−0.424694	−	0.905337i	$-0.639618\pi$
$661$	14.6983	−	25.4582i	0.571698	−	0.990209i	0.996392	−	0.0848723i	$-0.0270482\pi$
$662$	7.21212	−	12.4918i	0.280307	−	0.485506i
$663$	−0.609077	−	5.22907i	−0.0236546	−	0.203080i
$664$	−2.04433			−0.0793354
$665$	2.25919	−	3.91303i	0.0876077	−	0.151741i
$666$	−3.15515	+	10.5084i	−0.122259	+	0.407192i
$667$	−9.61813			−0.372415
$668$	3.20854	+	5.55736i	0.124142	+	0.215021i
$669$	4.25863	+	36.5614i	0.164648	+	1.41355i
$670$	15.7104			0.606944
$671$	27.6349	−	47.8651i	1.06684	−	1.84781i
$672$	0.781366	−	0.581221i	0.0301419	−	0.0224211i
$673$	13.8437			0.533634			0.266817	−	0.963747i	$-0.414028\pi$
$673$	13.8437			0.533634			0.266817	+	0.963747i	$0.414028\pi$
$674$	−27.4621			−1.05780
$675$	−8.77905	+	10.4371i	−0.337906	+	0.401723i
$676$	5.41900	−	9.38598i	0.208423	−	0.360999i
$677$	48.5912			1.86751			0.933755	−	0.357912i	$-0.116511\pi$
$677$	48.5912			1.86751			0.933755	+	0.357912i	$0.116511\pi$
$678$	−2.74934	−	23.6037i	−0.105588	−	0.906496i
$679$	8.93862			0.343033
$680$	−2.85393	−	4.94316i	−0.109443	−	0.189561i
$681$	42.1995	+	18.2230i	1.61709	+	0.698308i
$682$	−7.37358	−	20.9669i	−0.282349	−	0.802866i
$683$	12.4018			0.474540			0.237270	−	0.971444i	$-0.423747\pi$
$683$	12.4018			0.474540			0.237270	+	0.971444i	$0.423747\pi$
$684$	−5.98657	−	6.35555i	−0.228902	−	0.243010i
$685$	−2.30415	+	3.99091i	−0.0880371	+	0.152485i
$686$	3.84683	−	6.66291i	0.146873	−	0.254391i
$687$	3.22609	+	1.39312i	0.123083	+	0.0531510i
$688$	11.7512			0.448011
$689$	2.15186			0.0819795
$690$	8.61019	−	6.40471i	0.327784	−	0.243823i
$691$	−19.2775			−0.733351			−0.366675	−	0.930349i	$-0.619504\pi$
$691$	−19.2775			−0.733351			−0.366675	+	0.930349i	$0.619504\pi$
$692$	10.5109	+	18.2054i	0.399563	+	0.692064i
$693$	−1.93624	+	6.44877i	−0.0735518	+	0.244969i
$694$	4.93173	−	8.54200i	0.187206	−	0.324250i
$695$	45.7312			1.73468
$696$	−5.95731	+	4.43136i	−0.225811	+	0.167970i
$697$	6.44781	+	11.1679i	0.244228	+	0.423016i
$698$	5.34850	+	9.26388i	0.202444	+	0.350643i
$699$	−20.5852	−	8.88932i	−0.778603	−	0.336225i
$700$	1.47572			0.0557769
$701$	−21.8284	+	37.8079i	−0.824447	+	1.42798i	0.0778936	+	0.996962i	$0.475181\pi$
$701$	−21.8284	+	37.8079i	−0.824447	+	1.42798i	−0.902341	+	0.431023i	$0.858153\pi$
$702$	4.91809	−	5.84692i	0.185621	−	0.220678i
$703$	−5.32202	−	9.21800i	−0.200724	−	0.347664i
$704$	−3.99186			−0.150449
$705$	−3.28521	−	28.2043i	−0.123728	−	1.06224i
$706$	29.0758			1.09428
$707$	−1.18531			−0.0445781
$708$	−0.254746	−	2.18706i	−0.00957393	−	0.0821946i
$709$	0.117091	−	0.202808i	0.00439746	−	0.00761662i	−0.863818	−	0.503803i	$-0.831934\pi$
$709$	0.117091	−	0.202808i	0.00439746	−	0.00761662i	0.868216	+	0.496187i	$0.165267\pi$
$710$	5.93206	−	10.2746i	0.222626	−	0.385600i
$711$	−0.890524	+	2.96594i	−0.0333973	+	0.111232i
$712$	−3.63785			−0.136334
$713$	−12.2784	−	2.30326i	−0.459830	−	0.0862578i
$714$	1.61517	−	1.20145i	0.0604461	−	0.0449630i
$715$	−8.10372	−	14.0361i	−0.303062	−	0.524919i
$716$	−15.1926			−0.567775
$717$	19.2255	−	14.3009i	0.717989	−	0.534078i
$718$	−3.58934			−0.133953
$719$	−22.2177	+	38.4822i	−0.828580	+	1.43514i	0.0705720	+	0.997507i	$0.477518\pi$
$719$	−22.2177	+	38.4822i	−0.828580	+	1.43514i	−0.899152	+	0.437636i	$0.855816\pi$
$720$	2.38217	−	7.93395i	0.0887781	−	0.295681i
$721$	−6.62631			−0.246777
$722$	−10.5298			−0.391877
$723$	−5.58298	−	47.9313i	−0.207633	−	1.78258i
$724$	−1.37767	+	2.38619i	−0.0512007	+	0.0886822i
$725$	−11.2512			−0.417859
$726$	6.85820	−	5.10149i	0.254532	−	0.189334i
$727$	−5.06156	−	8.76688i	−0.187723	−	0.325145i	0.756768	−	0.653684i	$-0.226777\pi$
$727$	−5.06156	−	8.76688i	−0.187723	−	0.325145i	−0.944491	+	0.328538i	$0.893444\pi$
$728$	−0.826708			−0.0306398
$729$	−20.7247	+	17.3057i	−0.767581	+	0.640952i
$730$	−12.9019	+	22.3468i	−0.477522	+	0.827093i
$731$	24.2910			0.898436
$732$	−22.0163	−	9.50733i	−0.813746	−	0.351401i
$733$	−16.8826	+	29.2415i	−0.623574	+	1.08006i	0.365241	+	0.930913i	$0.380986\pi$
$733$	−16.8826	+	29.2415i	−0.623574	+	1.08006i	−0.988815	+	0.149148i	$0.952347\pi$
$734$	7.34444	−	12.7209i	0.271088	−	0.469539i
$735$	−3.69847	−	31.7522i	−0.136420	−	1.17120i
$736$	−1.12187	+	1.94313i	−0.0413525	+	0.0716247i
$737$	11.3559	−	19.6689i	0.418298	−	0.724514i
$738$	−5.38196	+	17.9250i	−0.198113	+	0.659827i
$739$	12.3038	+	21.3109i	0.452604	+	0.783934i	0.998547	−	0.0538888i	$-0.0171616\pi$
$739$	12.3038	+	21.3109i	0.452604	+	0.783934i	−0.545943	+	0.837823i	$0.683828\pi$
$740$	5.04940	−	8.74582i	0.185620	−	0.321503i
$741$	0.857546	+	7.36224i	0.0315027	+	0.270459i
$742$	0.411416	+	0.712593i	0.0151035	+	0.0261601i
$743$	7.66651	+	13.2788i	0.281257	+	0.487152i	0.971695	−	0.236240i	$-0.0759153\pi$
$743$	7.66651	+	13.2788i	0.281257	+	0.487152i	−0.690438	+	0.723392i	$0.742582\pi$
$744$	−8.66623	+	4.23043i	−0.317719	+	0.155095i
$745$	17.5940	−	30.4737i	0.644594	−	1.11647i
$746$	38.4484			1.40770
$747$	−4.20515	−	4.46433i	−0.153858	−	0.163341i
$748$	−8.25158			−0.301708
$749$	3.45042			0.126076
$750$	−9.11508	+	6.78028i	−0.332836	+	0.247581i
$751$	−35.9315			−1.31116			−0.655580	−	0.755126i	$-0.727576\pi$
$751$	−35.9315			−1.31116			−0.655580	+	0.755126i	$0.727576\pi$
$752$	2.96852	+	5.14163i	0.108251	+	0.187496i
$753$	−12.1259	+	9.01987i	−0.441892	+	0.328702i
$754$	6.30301			0.229542
$755$	−5.97908	−	10.3561i	−0.217601	−	0.376896i
$756$	2.87651	+	0.510756i	0.104618	+	0.0185760i
$757$	−6.91512	−	11.9773i	−0.251334	−	0.435324i	0.712559	−	0.701612i	$-0.247536\pi$
$757$	−6.91512	−	11.9773i	−0.251334	−	0.435324i	−0.963893	+	0.266288i	$0.914203\pi$
$758$	−13.8582	−	24.0031i	−0.503353	−	0.871833i
$759$	−1.79485	−	15.4092i	−0.0651488	−	0.559318i
$760$	4.01818	+	6.95968i	0.145755	+	0.252454i
$761$	21.8022			0.790331			0.395165	−	0.918610i	$-0.370687\pi$
$761$	21.8022			0.790331			0.395165	+	0.918610i	$0.370687\pi$
$762$	1.43163	+	12.2909i	0.0518626	+	0.445253i
$763$	−3.61643	−	6.26385i	−0.130924	−	0.226766i
$764$	−8.80426	−	15.2494i	−0.318527	−	0.551705i
$765$	4.92419	−	16.4003i	0.178034	−	0.592954i
$766$	−11.0303	−	19.1051i	−0.398542	−	0.690295i
$767$	−0.934595	+	1.61877i	−0.0337463	+	0.0584503i
$768$	0.200393	+	1.72042i	0.00723104	+	0.0620803i
$769$	−11.3437			−0.409066			−0.204533	−	0.978860i	$-0.565568\pi$
$769$	−11.3437			−0.409066			−0.204533	+	0.978860i	$0.565568\pi$
$770$	3.09871	−	5.36712i	0.111670	−	0.193417i
$771$	9.00615	−	6.69925i	0.324348	−	0.241267i
$772$	−2.11290	−	3.65965i	−0.0760450	−	0.131714i
$773$	45.7918			1.64702			0.823509	−	0.567303i	$-0.192013\pi$
$773$	45.7918			1.64702			0.823509	+	0.567303i	$0.192013\pi$
$774$	24.1721	+	25.6619i	0.868847	+	0.922398i
$775$	−14.3632	−	2.69433i	−0.515941	−	0.0967834i
$776$	−7.94907	+	13.7682i	−0.285355	+	0.494249i
$777$	3.26974	+	1.41198i	0.117301	+	0.0506544i
$778$	−2.74980			−0.0985852
$779$	−9.07815	−	15.7238i	−0.325259	−	0.563364i
$780$	−5.64248	+	4.19717i	−0.202033	+	0.150283i
$781$	−8.57569	−	14.8535i	−0.306862	−	0.531501i
$782$	−2.31901	+	4.01665i	−0.0829277	+	0.143635i
$783$	−21.9311	−	3.89412i	−0.783755	−	0.139164i
$784$	3.34194	+	5.78841i	0.119355	+	0.206729i
$785$	61.1951			2.18415
$786$	4.84254	−	3.60214i	0.172728	−	0.128484i
$787$	7.58536			0.270389			0.135194	−	0.990819i	$-0.456834\pi$
$787$	7.58536			0.270389			0.135194	+	0.990819i	$0.456834\pi$
$788$	−11.0548	+	19.1475i	−0.393812	+	0.682103i
$789$	−21.9597	+	16.3348i	−0.781786	+	0.581534i
$790$	1.42517	−	2.46846i	0.0507052	−	0.0878240i
$791$	−7.71384			−0.274273
$792$	−8.21118	−	8.71727i	−0.291772	−	0.309755i
$793$	10.1792	+	17.6308i	0.361472	+	0.626089i
$794$	−0.820424	−	1.42102i	−0.0291158	−	0.0504300i
$795$	6.42582	+	2.77487i	0.227900	+	0.0984145i
$796$	−4.22595	+	7.31956i	−0.149785	+	0.259435i
$797$	14.8039	−	25.6410i	0.524380	−	0.908253i	−0.475217	−	0.879869i	$-0.657631\pi$
$797$	14.8039	−	25.6410i	0.524380	−	0.908253i	0.999597	−	0.0283841i	$-0.00903614\pi$
$798$	−2.27406	+	1.69157i	−0.0805009	+	0.0598808i
$799$	6.13624	+	10.6283i	0.217085	+	0.376002i
$800$	−1.31235	+	2.27306i	−0.0463986	+	0.0803647i
$801$	−7.48299	−	7.94419i	−0.264398	−	0.280694i
$802$	9.79122			0.345740
$803$	18.6517	+	32.3057i	0.658204	+	1.14004i
$804$	−9.04702	−	3.90679i	−0.319064	−	0.137782i
$805$	−1.74171	−	3.01673i	−0.0613873	−	0.106326i
$806$	8.04636	+	1.50939i	0.283421	+	0.0531658i
$807$	2.10219	+	18.0478i	0.0740005	+	0.635312i
$808$	1.05409	−	1.82574i	0.0370827	−	0.0642292i
$809$	21.6194	−	37.4460i	0.760099	−	1.31653i	−0.182700	−	0.983169i	$-0.558484\pi$
$809$	21.6194	−	37.4460i	0.760099	−	1.31653i	0.942799	−	0.333361i	$-0.108183\pi$
$810$	22.2259	−	11.1179i	0.780940	−	0.390644i
$811$	−22.3906	−	38.7817i	−0.786241	−	1.36181i	−0.928255	−	0.371944i	$-0.878691\pi$
$811$	−22.3906	−	38.7817i	−0.786241	−	1.36181i	0.142015	−	0.989865i	$-0.454642\pi$
$812$	1.20507	+	2.08725i	0.0422898	+	0.0732481i
$813$	−30.4152	−	13.1342i	−1.06671	−	0.460638i
$814$	−7.29967	−	12.6434i	−0.255853	−	0.443151i
$815$	−2.51722	+	4.35995i	−0.0881743	+	0.152722i
$816$	0.414232	+	3.55629i	0.0145010	+	0.124495i
$817$	−34.2004			−1.19652
$818$	−8.38880	+	14.5298i	−0.293308	+	0.508024i
$819$	−1.70052	−	1.80533i	−0.0594211	−	0.0630835i
$820$	8.61313	−	14.9184i	0.300784	−	0.520973i
$821$	0.261194	−	0.452402i	0.00911574	−	0.0157889i	−0.861432	−	0.507874i	$-0.830432\pi$
$821$	0.261194	−	0.452402i	0.00911574	−	0.0157889i	0.870547	+	0.492085i	$0.163765\pi$
$822$	2.31932	−	1.72523i	0.0808955	−	0.0601744i
$823$	5.13594			0.179028			0.0895138	−	0.995986i	$-0.471469\pi$
$823$	5.13594			0.179028			0.0895138	+	0.995986i	$0.471469\pi$
$824$	5.89275	−	10.2065i	0.205284	−	0.355562i
$825$	−2.09960	−	18.0256i	−0.0730986	−	0.627569i
$826$	−0.714742			−0.0248691
$827$	−18.1801	−	31.4889i	−0.632185	−	1.09498i	−0.987104	−	0.160079i	$-0.948825\pi$
$827$	−18.1801	−	31.4889i	−0.632185	−	1.09498i	0.354919	−	0.934897i	$-0.384508\pi$
$828$	−6.55099	+	1.54709i	−0.227663	+	0.0537652i
$829$	36.4298			1.26526			0.632630	−	0.774454i	$-0.281975\pi$
$829$	36.4298			1.26526			0.632630	+	0.774454i	$0.281975\pi$
$830$	2.82249	+	4.88869i	0.0979700	+	0.169689i
$831$	7.37239	−	5.48397i	0.255745	−	0.190237i
$832$	0.735188	−	1.27338i	0.0254880	−	0.0441466i
$833$	6.90814	+	11.9653i	0.239353	+	0.414571i
$834$	−26.3349	−	11.3722i	−0.911903	−	0.393788i
$835$	8.85971	−	15.3455i	0.306603	−	0.531052i
$836$	11.6178			0.401809
$837$	−27.0645	−	10.2231i	−0.935487	−	0.353360i
$838$	−23.5366			−0.813058
$839$	2.42087	−	4.19306i	0.0835776	−	0.144761i	−0.821207	−	0.570631i	$-0.806699\pi$
$839$	2.42087	−	4.19306i	0.0835776	−	0.144761i	0.904784	+	0.425870i	$0.140032\pi$
$840$	−2.46869	−	1.06606i	−0.0851778	−	0.0367824i
$841$	5.31225	+	9.20108i	0.183181	+	0.317279i
$842$	−17.7261	+	30.7024i	−0.610880	+	1.05808i
$843$	−31.5725	+	23.4853i	−1.08742	+	0.808877i
$844$	−13.3678	−	23.1538i	−0.460140	−	0.796985i
$845$	−29.9268			−1.02951
$846$	−5.12190	+	17.0588i	−0.176094	+	0.586493i
$847$	−1.38731	−	2.40289i	−0.0476686	−	0.0825644i
$848$	−1.46348			−0.0502561
$849$	−5.13098	−	44.0507i	−0.176095	−	1.51182i
$850$	−2.71276	+	4.69864i	−0.0930470	+	0.161162i
$851$	−8.20596			−0.281297
$852$	−5.97111	+	4.44162i	−0.204567	+	0.152167i
$853$	−4.69259	+	8.12781i	−0.160671	+	0.278291i	−0.935110	−	0.354359i	$-0.884699\pi$
$853$	−4.69259	+	8.12781i	−0.160671	+	0.278291i	0.774438	+	0.632649i	$0.218033\pi$
$854$	−3.89231	+	6.74168i	−0.133192	+	0.230696i
$855$	−6.93298	+	23.0907i	−0.237103	+	0.789685i
$856$	−3.06844	+	5.31470i	−0.104877	+	0.181653i
$857$	−39.3604			−1.34453			−0.672263	−	0.740312i	$-0.734678\pi$
$857$	−39.3604			−1.34453			−0.672263	+	0.740312i	$0.734678\pi$
$858$	1.17621	+	10.0980i	0.0401551	+	0.344742i
$859$	−2.24672	+	3.89143i	−0.0766570	+	0.132774i	−0.901806	−	0.432142i	$-0.857758\pi$
$859$	−2.24672	+	3.89143i	−0.0766570	+	0.132774i	0.825149	+	0.564916i	$0.191091\pi$
$860$	−16.2242	−	28.1012i	−0.553242	−	0.958244i
$861$	5.57744	+	2.40851i	0.190079	+	0.0820818i
$862$	−10.4796	−	18.1512i	−0.356937	−	0.618233i
$863$	11.5510	+	20.0070i	0.393202	+	0.681045i	0.992870	−	0.119203i	$-0.0380341\pi$
$863$	11.5510	+	20.0070i	0.393202	+	0.681045i	−0.599668	+	0.800249i	$0.704701\pi$
$864$	−3.34478	+	3.97648i	−0.113792	+	0.135283i
$865$	29.0235	−	50.2702i	0.986829	−	1.70924i
$866$	3.04820	−	5.27963i	0.103582	−	0.179409i
$867$	−2.55041	−	21.8959i	−0.0866165	−	0.743624i
$868$	1.03855	+	2.95314i	0.0352507	+	0.100236i
$869$	−2.06030	−	3.56854i	−0.0698908	−	0.121054i
$870$	18.8218	+	8.12785i	0.638120	+	0.275560i
$871$	4.18286	+	7.24492i	0.141731	+	0.245485i
$872$	12.8643			0.435640
$873$	−46.4176	+	10.9621i	−1.57100	+	0.371010i
$874$	3.26504	−	5.65521i	0.110442	−	0.191290i
$875$	1.84384	+	3.19363i	0.0623333	+	0.107964i
$876$	12.9869	−	9.66031i	0.438785	−	0.326392i
$877$	−23.7542	+	41.1436i	−0.802124	+	1.38932i	0.116092	+	0.993238i	$0.462963\pi$
$877$	−23.7542	+	41.1436i	−0.802124	+	1.38932i	−0.918216	+	0.396081i	$0.870370\pi$
$878$	13.8876	−	24.0540i	0.468683	−	0.811782i
$879$	10.0903	+	4.35732i	0.340338	+	0.146969i
$880$	5.51133	+	9.54590i	0.185787	+	0.321792i
$881$	−27.7949	−	48.1423i	−0.936435	−	1.62195i	−0.772054	−	0.635557i	$-0.780771\pi$
$881$	−27.7949	−	48.1423i	−0.936435	−	1.62195i	−0.164381	−	0.986397i	$-0.552563\pi$
$882$	−5.76620	+	19.2047i	−0.194158	+	0.646655i
$883$	1.92102			0.0646475			0.0323238	−	0.999477i	$-0.489709\pi$
$883$	1.92102			0.0646475			0.0323238	+	0.999477i	$0.489709\pi$
$884$	1.51971	−	2.63221i	0.0511134	−	0.0885309i
$885$	−4.87829	+	3.62873i	−0.163982	+	0.121978i
$886$	−1.51177	+	2.61845i	−0.0507888	+	0.0879687i
$887$	−24.1943			−0.812366			−0.406183	−	0.913792i	$-0.633140\pi$
$887$	−24.1943			−0.812366			−0.406183	+	0.913792i	$0.633140\pi$
$888$	−5.08264	+	3.78073i	−0.170562	+	0.126873i
$889$	4.01675			0.134717
$890$	5.02257	+	8.69934i	0.168357	+	0.291603i
$891$	2.14617	−	35.8625i	0.0718996	−	1.20144i
$892$	−10.6257	+	18.4043i	−0.355776	+	0.616222i
$893$	−8.63948	−	14.9640i	−0.289109	−	0.500752i
$894$	−17.7098	+	13.1735i	−0.592304	+	0.440587i
$895$	20.9756	+	36.3308i	0.701137	+	1.21440i
$896$	0.562243			0.0187832
$897$	5.24602	+	2.26539i	0.175159	+	0.0756393i
$898$	13.3146	−	23.0615i	0.444313	−	0.769572i
$899$	−7.91814	−	22.5154i	−0.264085	−	0.750931i
$900$	−7.66329	+	1.80978i	−0.255443	+	0.0603259i
$901$	−3.02516			−0.100783
$902$	−12.4516	−	21.5668i	−0.414593	−	0.718095i
$903$	9.18201	−	6.83006i	0.305558	−	0.227290i
$904$	6.85988	−	11.8817i	0.228156	−	0.395178i
$905$	7.60828			0.252908
$906$	0.867830	+	7.45053i	0.0288317	+	0.247527i
$907$	9.28510	−	16.0823i	0.308307	−	0.534003i	−0.669685	−	0.742645i	$-0.733571\pi$
$907$	9.28510	−	16.0823i	0.308307	−	0.534003i	0.977992	+	0.208642i	$0.0669043\pi$
$908$	13.2692	+	22.9830i	0.440355	+	0.762718i
$909$	6.15522	−	1.45363i	0.204156	−	0.0482138i
$910$	1.14139	+	1.97694i	0.0378367	+	0.0655350i
$911$	20.8285	+	36.0760i	0.690079	+	1.19525i	0.971811	+	0.235759i	$0.0757577\pi$
$911$	20.8285	+	36.0760i	0.690079	+	1.19525i	−0.281732	+	0.959493i	$0.590909\pi$
$912$	−0.583216	−	5.00705i	−0.0193122	−	0.165800i
$913$	8.16067			0.270079
$914$	6.35410	+	11.0056i	0.210175	+	0.364034i
$915$	7.66137	+	65.7748i	0.253277	+	2.17445i
$916$	1.01441	+	1.75702i	0.0335172	+	0.0580535i
$917$	−0.979572	−	1.69667i	−0.0323483	−	0.0560290i
$918$	−6.91402	+	8.21981i	−0.228197	+	0.271294i
$919$	−17.9232	−	31.0439i	−0.591231	−	1.02404i	−0.994067	−	0.108770i	$-0.965309\pi$
$919$	−17.9232	−	31.0439i	−0.591231	−	1.02404i	0.402836	−	0.915272i	$-0.368025\pi$
$920$	6.19558			0.204262
$921$	−7.45905	+	5.54843i	−0.245784	+	0.182827i
$922$	10.5442	+	18.2631i	0.347255	+	0.601463i
$923$	6.31760			0.207946
$924$	−3.11910	+	2.32015i	−0.102611	+	0.0763274i
$925$	−9.59927			−0.315622
$926$	16.6791			0.548109
$927$	34.4099	−	8.12632i	1.13017	−	0.266903i
$928$	−4.28667			−0.140717
$929$	−14.7317	+	25.5161i	−0.483333	+	0.837157i	−0.999817	−	0.0191398i	$-0.993907\pi$
$929$	−14.7317	+	25.5161i	−0.483333	+	0.837157i	0.516484	+	0.856297i	$0.327241\pi$
$930$	22.0814	+	14.8832i	0.724077	+	0.488040i
$931$	−9.72627	−	16.8464i	−0.318766	−	0.552118i
$932$	−6.47283	−	11.2113i	−0.212024	−	0.367237i
$933$	5.74959	+	49.3616i	0.188233	+	1.61603i
$934$	17.2199	−	29.8257i	0.563451	−	0.975925i
$935$	11.3925	+	19.7324i	0.372574	+	0.645318i
$936$	4.29303	−	1.01385i	0.140322	−	0.0331388i
$937$	6.46800	−	11.2029i	0.211300	−	0.365983i	−0.740821	−	0.671702i	$-0.765563\pi$
$937$	6.46800	−	11.2029i	0.211300	−	0.365983i	0.952122	+	0.305719i	$0.0988968\pi$
$938$	−1.59944	+	2.77032i	−0.0522237	+	0.0904541i
$939$	1.40865	+	12.0936i	0.0459694	+	0.394659i
$940$	8.19693	−	14.1975i	0.267354	−	0.463071i
$941$	26.5819	−	46.0413i	0.866546	−	1.50090i	0.00104283	−	0.999999i	$-0.499668\pi$
$941$	26.5819	−	46.0413i	0.866546	−	1.50090i	0.865504	−	0.500903i	$-0.166999\pi$
$942$	−35.2400	−	15.2177i	−1.14818	−	0.495821i
$943$	−13.9975			−0.455822
$944$	0.635617	−	1.10092i	0.0206876	−	0.0358319i
$945$	−2.75004	−	7.58389i	−0.0894587	−	0.246704i
$946$	−46.9092			−1.52515
$947$	22.3097	+	38.6415i	0.724968	+	1.25568i	0.958987	+	0.283450i	$0.0914788\pi$
$947$	22.3097	+	38.6415i	0.724968	+	1.25568i	−0.234019	+	0.972232i	$0.575188\pi$
$948$	−1.43455	+	1.06709i	−0.0465920	+	0.0346576i
$949$	−13.7405			−0.446035
$950$	3.81942	−	6.61542i	0.123918	−	0.214633i
$951$	1.17374	+	10.0768i	0.0380610	+	0.326763i
$952$	1.16222			0.0376676
$953$	28.5363			0.924382			0.462191	−	0.886780i	$-0.347063\pi$
$953$	28.5363			0.924382			0.462191	+	0.886780i	$0.347063\pi$
$954$	−3.01035	−	3.19589i	−0.0974638	−	0.103471i
$955$	−24.3111	+	42.1080i	−0.786688	+	1.36258i
$956$	13.8340			0.447423
$957$	23.7807	−	17.6894i	0.768722	−	0.571816i
$958$	25.2674			0.816354
$959$	−0.469163	−	0.812615i	−0.0151501	−	0.0262407i
$960$	3.83744	−	2.85449i	0.123853	−	0.0921283i
$961$	−4.71644	−	30.6391i	−0.152143	−	0.988358i
$962$	5.37758			0.173380
$963$	−17.9178	+	4.23150i	−0.577393	+	0.136358i
$964$	13.9301	−	24.1277i	0.448659	−	0.777100i
$965$	−5.83433	+	10.1054i	−0.187814	+	0.325303i
$966$	0.252800	+	2.17035i	0.00813370	+	0.0698298i
$967$	−12.6640			−0.407245			−0.203623	−	0.979049i	$-0.565272\pi$
$967$	−12.6640			−0.407245			−0.203623	+	0.979049i	$0.565272\pi$
$968$	4.93492			0.158614
$969$	−1.20557	−	10.3501i	−0.0387284	−	0.332493i
$970$	43.8993			1.40952
$971$	18.7126	+	32.4111i	0.600515	+	1.04012i	0.992743	+	0.120255i	$0.0383712\pi$
$971$	18.7126	+	32.4111i	0.600515	+	1.04012i	−0.392228	+	0.919868i	$0.628295\pi$
$972$	−15.5639	+	0.875349i	−0.499211	+	0.0280768i
$973$	−4.65581	+	8.06410i	−0.149258	+	0.258523i
$974$	27.8791			0.893303
$975$	6.13675	+	2.65004i	0.196533	+	0.0848692i
$976$	−6.92283	−	11.9907i	−0.221594	−	0.383813i
$977$	20.4535	+	35.4264i	0.654364	+	1.13339i	0.982053	+	0.188606i	$0.0603969\pi$
$977$	20.4535	+	35.4264i	0.654364	+	1.13339i	−0.327689	+	0.944786i	$0.606270\pi$
$978$	2.53379	−	1.88476i	0.0810216	−	0.0602681i
$979$	14.5218			0.464117
$980$	9.22805	−	15.9835i	0.294779	−	0.510573i
$981$	26.4617	+	28.0926i	0.844856	+	0.896927i
$982$	−1.00378	−	1.73860i	−0.0320319	−	0.0554809i
$983$	19.5580			0.623802			0.311901	−	0.950115i	$-0.399034\pi$
$983$	19.5580			0.623802			0.311901	+	0.950115i	$0.399034\pi$
$984$	−8.66983	+	6.44908i	−0.276384	+	0.205589i
$985$	61.0511			1.94525
$986$	−8.86099			−0.282191
$987$	5.30793	+	2.29213i	0.168953	+	0.0729592i
$988$	−2.13966	+	3.70601i	−0.0680718	+	0.117904i
$989$	−13.1833	+	22.8341i	−0.419204	+	0.726083i
$990$	−9.50927	+	31.6712i	−0.302224	+	1.00658i
$991$	17.9448			0.570035			0.285018	−	0.958522i	$-0.408001\pi$
$991$	17.9448			0.570035			0.285018	+	0.958522i	$0.408001\pi$
$992$	−5.47232	−	1.02653i	−0.173746	−	0.0325924i
$993$	22.9363	+	9.90462i	0.727862	+	0.314313i
$994$	1.20786	+	2.09208i	0.0383111	+	0.0663568i
$995$	23.3381			0.739868
$996$	−0.409669	−	3.51710i	−0.0129808	−	0.111444i
$997$	13.6427			0.432070			0.216035	−	0.976386i	$-0.430688\pi$
$997$	13.6427			0.432070			0.216035	+	0.976386i	$0.430688\pi$
$998$	10.2613	−	17.7731i	0.324817	−	0.562599i
$999$	−18.7111	−	3.32237i	−0.591994	−	0.105115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.g.a.439.3	yes	32
3.2	odd	2		1674.2.g.b.1369.13		32
9.4	even	3		558.2.h.a.67.14	yes	32
9.5	odd	6		1674.2.h.b.253.4		32
31.25	even	3		558.2.h.a.25.14	yes	32
93.56	odd	6		1674.2.h.b.397.4		32
279.149	odd	6		1674.2.g.b.955.13		32
279.211	even	3	inner	558.2.g.a.211.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.g.a.211.3	✓	32	279.211	even	3	inner
558.2.g.a.439.3	yes	32	1.1	even	1	trivial
558.2.h.a.25.14	yes	32	31.25	even	3
558.2.h.a.67.14	yes	32	9.4	even	3
1674.2.g.b.955.13		32	279.149	odd	6
1674.2.g.b.1369.13		32	3.2	odd	2
1674.2.h.b.253.4		32	9.5	odd	6
1674.2.h.b.397.4		32	93.56	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.59012 - 0.686665i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.38064 + 2.39134i) q^{5} +(1.38973 - 1.03375i) q^{6} +(-0.281122 - 0.486917i) q^{7} +1.00000 q^{8} +(2.05698 + 2.18376i) q^{9} +(-1.38064 - 2.39134i) q^{10} -3.99186 q^{11} +(0.200393 + 1.72042i) q^{12} +(0.735188 - 1.27338i) q^{13} +0.562243 q^{14} +(3.83744 - 2.85449i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.03355 + 1.79016i) q^{17} +(-2.91969 + 0.689519i) q^{18} +(1.45518 - 2.52045i) q^{19} +2.76129 q^{20} +(0.112669 + 0.967294i) q^{21} +(1.99593 - 3.45705i) q^{22} +(-1.12187 - 1.94313i) q^{23} +(-1.59012 - 0.686665i) q^{24} +(-1.31235 - 2.27306i) q^{25} +(0.735188 + 1.27338i) q^{26} +(-1.77134 - 4.88491i) q^{27} +(-0.281122 + 0.486917i) q^{28} +(2.14333 - 3.71236i) q^{29} +(0.553341 + 4.75057i) q^{30} +(3.62516 - 4.22590i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(6.34754 + 2.74107i) q^{33} +(-1.03355 - 1.79016i) q^{34} +1.55251 q^{35} +(0.862702 - 2.87328i) q^{36} +(1.82864 - 3.16730i) q^{37} +(1.45518 + 2.52045i) q^{38} +(-2.04343 + 1.52001i) q^{39} +(-1.38064 + 2.39134i) q^{40} +(3.11925 - 5.40270i) q^{41} +(-0.894036 - 0.386072i) q^{42} +(-5.87561 - 10.1769i) q^{43} +(1.99593 + 3.45705i) q^{44} +(-8.06209 + 1.90396i) q^{45} +2.24373 q^{46} +(2.96852 - 5.14163i) q^{47} +(1.38973 - 1.03375i) q^{48} +(3.34194 - 5.78841i) q^{49} +2.62470 q^{50} +(2.87272 - 2.13688i) q^{51} -1.47038 q^{52} +(0.731740 + 1.26741i) q^{53} +(5.11613 + 0.908425i) q^{54} +(5.51133 - 9.54590i) q^{55} +(-0.281122 - 0.486917i) q^{56} +(-4.04462 + 3.00860i) q^{57} +(2.14333 + 3.71236i) q^{58} -1.27123 q^{59} +(-4.39078 - 1.89608i) q^{60} +(-6.92283 + 11.9907i) q^{61} +(1.84716 + 5.25243i) q^{62} +(0.485048 - 1.61548i) q^{63} +1.00000 q^{64} +(2.03006 + 3.51617i) q^{65} +(-5.54760 + 4.12660i) q^{66} +(-2.84476 + 4.92726i) q^{67} +2.06710 q^{68} +(0.449627 + 3.86016i) q^{69} +(-0.776257 + 1.34452i) q^{70} +(2.14830 + 3.72096i) q^{71} +(2.05698 + 2.18376i) q^{72} +(-4.67244 - 8.09290i) q^{73} +(1.82864 + 3.16730i) q^{74} +(0.525970 + 4.51558i) q^{75} -2.91037 q^{76} +(1.12220 + 1.94370i) q^{77} +(-0.294652 - 2.52966i) q^{78} +(0.516125 + 0.893955i) q^{79} +(-1.38064 - 2.39134i) q^{80} +(-0.537638 + 8.98393i) q^{81} +(3.11925 + 5.40270i) q^{82} -2.04433 q^{83} +(0.781366 - 0.581221i) q^{84} +(-2.85393 - 4.94316i) q^{85} +11.7512 q^{86} +(-5.95731 + 4.43136i) q^{87} -3.99186 q^{88} -3.63785 q^{89} +(2.38217 - 7.93395i) q^{90} -0.826708 q^{91} +(-1.12187 + 1.94313i) q^{92} +(-8.66623 + 4.23043i) q^{93} +(2.96852 + 5.14163i) q^{94} +(4.01818 + 6.95968i) q^{95} +(0.200393 + 1.72042i) q^{96} +(-7.94907 + 13.7682i) q^{97} +(3.34194 + 5.78841i) q^{98} +(-8.21118 - 8.71727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} + 4 q^{3} - 16 q^{4} - q^{5} - 2 q^{6} + q^{7} + 32 q^{8} + 12 q^{9} - q^{10} + 4 q^{11} - 2 q^{12} - 10 q^{13} - 2 q^{14} - 13 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} + 4 q^{19} + 2 q^{20}+ \cdots + 19 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 + 4 * q^3 - 16 * q^4 - q^5 - 2 * q^6 + q^7 + 32 * q^8 + 12 * q^9 - q^10 + 4 * q^11 - 2 * q^12 - 10 * q^13 - 2 * q^14 - 13 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 + 4 * q^19 + 2 * q^20 + 10 * q^21 - 2 * q^22 - q^23 + 4 * q^24 - 19 * q^25 - 10 * q^26 + 7 * q^27 + q^28 - 3 * q^29 + 14 * q^30 - q^31 - 16 * q^32 - 7 * q^33 - 4 * q^34 - 6 * q^36 - 19 * q^37 + 4 * q^38 + 19 * q^39 - q^40 + 10 * q^41 - 11 * q^42 - 13 * q^43 - 2 * q^44 + 14 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 - 13 * q^49 + 38 * q^50 + 20 * q^51 + 20 * q^52 - 7 * q^53 - 17 * q^54 - 11 * q^55 + q^56 - 5 * q^57 - 3 * q^58 + 12 * q^59 - q^60 + 7 * q^61 + 11 * q^62 - 42 * q^63 + 32 * q^64 - 8 * q^65 + 5 * q^66 - 8 * q^67 + 8 * q^68 + 43 * q^69 + 7 * q^71 + 12 * q^72 + 7 * q^73 - 19 * q^74 - 41 * q^75 - 8 * q^76 - q^77 - 11 * q^78 - 34 * q^79 - q^80 + 10 * q^82 - 28 * q^83 + q^84 + 13 * q^85 + 26 * q^86 - 54 * q^87 + 4 * q^88 + 2 * q^89 - 19 * q^90 + 24 * q^91 - q^92 - 15 * q^93 - 6 * q^94 + 21 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + 19 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more